Linear Algebra with Applications (2-Download)
5th Edition
ISBN: 9780321796974
Author: Otto Bretscher
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 7.5, Problem 23E
Find all complex eigenvalues of the matrices in Exercises 20 through 26 (including the real ones, of course). Do not use technology. Show all your work.
23.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
a
Question 7. If det d e f
ghi
V3
= 2. Find det
-1
2
Question 8. Let A = 1
4
5
0
3
2.
1 Find adj (A)
2 Find det (A)
3
Find A-1
2g 2h 2i
-e-f
-d
273
2a 2b 2c
Question 1. Solve the system
-
x1 x2 + 3x3 + 2x4
-x1 + x22x3 + x4
2x12x2+7x3+7x4
Question 2. Consider the system
= 1
=-2
= 1
3x1 - x2 + ax3
= 1
x1 + 3x2 + 2x3
x12x2+2x3
= -b
= 4
1 For what values of a, b will the system be inconsistent?
2 For what values of a, b will the system have only one solution?
For what values of a, b will the saystem have infinitely many solutions?
Question 5. Let A, B, C ben x n-matrices, S is nonsigular. If A = S-1 BS, show that
det (A) = det (B)
Question 6. For what values of k is the matrix A = (2- k
-1
-1
2) singular?
k
Chapter 7 Solutions
Linear Algebra with Applications (2-Download)
Ch. 7.1 - In Exercises 1 through 4, let A be an invertible...Ch. 7.1 - In Exercises 1 through 4, let A be an invertible...Ch. 7.1 - In Exercises 1 through 4, let A be an invertible...Ch. 7.1 - In Exercises 1 through 4, let A be an invertible...Ch. 7.1 - If a vector is an eigenvector of both A and B, is...Ch. 7.1 - If a vector is an eigenvector of both A and B, is...Ch. 7.1 - If a vector is an eigenvector of the nnmatrixA...Ch. 7.1 - Find all 22 matrix for which e1=[10] is an...Ch. 7.1 - Find all 22 matrix for which e1 is an eigenvector.Ch. 7.1 - Find all 22 matrix for which [12] is an...
Ch. 7.1 - Find all 22 matrix for which [23] is an...Ch. 7.1 - Consider the matrix A=[2034] . Show that 2 and 4...Ch. 7.1 - Show that 4 is an eigenvalue of A=[661513] and...Ch. 7.1 - Find all 44 matrices for which e2 is an...Ch. 7.1 - Arguing geometrically, find all eigenvectors and...Ch. 7.1 - Arguing geometrically, find all eigenvectors and...Ch. 7.1 - Arguing geometrically, find all eigenvectors and...Ch. 7.1 - Arguing geometrically, find all eigenvectors and...Ch. 7.1 - Arguing geometrically, find all eigenvectors and...Ch. 7.1 - Arguing geometrically, find all eigenvectors and...Ch. 7.1 - Arguing geometrically, find all eigenvectors and...Ch. 7.1 - Arguing geometrically, find all eigenvectors and...Ch. 7.1 - Use matrix products to prove the following: If...Ch. 7.1 - In Exercises 24 through 29, consider a dynamical...Ch. 7.1 - In Exercises 24 through 29, consider a dynamical...Ch. 7.1 - In Exercises 24 through 29, consider a dynamical...Ch. 7.1 - In Exercises 24 through 29, consider a dynamical...Ch. 7.1 - In Exercises 24 through 29, consider a dynamical...Ch. 7.1 - In Exercises 24 through 29, consider a dynamical...Ch. 7.1 - In Exercises 30 through 32, consider the dynamical...Ch. 7.1 - In Exercises 30 through 32, consider the dynamical...Ch. 7.1 - In Exercises 30 through 32, consider the dynamical...Ch. 7.1 - Find a 22 matrix A such that x(t)=[ 2 t 6 t 2 t+ 6...Ch. 7.1 - Suppose is an eigenvector of the nn matrix A,with...Ch. 7.1 - Show that similar matrices have the same...Ch. 7.1 - Find a 22 matrix A such that [31] and [12] are...Ch. 7.1 - Consider the matrix A=[3443] a. Use the geometric...Ch. 7.1 - We are told that [111] is an eigenvector of the...Ch. 7.1 - Find a basis of the linear space V of all 22...Ch. 7.1 - Find a basis of the linear space V of all 22...Ch. 7.1 - Find a basis of the linear space V of all 22...Ch. 7.1 - Find a basis of the linear space V of all 33...Ch. 7.1 - Consider the linear space V of all nn matrices for...Ch. 7.1 - For nn , find the dimension of the space of all nn...Ch. 7.1 - If is any nonzero vector in 2 , what is the...Ch. 7.1 - If is an eigenvector of matrix A with associated...Ch. 7.1 - If is an eigenvector of matrix A, show that is...Ch. 7.1 - If A is a matrix of rank 1, show that any nonzero...Ch. 7.1 - Give an example of a matrix A of rank 1 that fails...Ch. 7.1 - Find an eigenbasis for each of the matrices A in...Ch. 7.1 - Find an eigenbasis for each of the matrices A in...Ch. 7.1 - Find an eigenbasis for each of the matrices A in...Ch. 7.1 - Find an eigenbasis for each of the matrices A in...Ch. 7.1 - Find an eigenbasis for each of the matrices A in...Ch. 7.1 - Arguing geometrically, find an eigenbasis for each...Ch. 7.1 - Arguing geometrically, find an eigenbasis for each...Ch. 7.1 - Arguing geometrically, find an eigenbasis for each...Ch. 7.1 - Arguing geometrically, find an eigenbasis for each...Ch. 7.1 - Arguing geometrically, find an eigenbasis for each...Ch. 7.1 - Arguing geometrically, find an eigenbasis for each...Ch. 7.1 - Arguing geometrically, find an eigenbasis for each...Ch. 7.1 - Arguing geometrically, find an eigenbasis for each...Ch. 7.1 - Arguing geometrically, find an eigenbasis for each...Ch. 7.1 - In all parts of this problem, let V be the linear...Ch. 7.1 - Consider an nn matrix A. A subspace V of n is...Ch. 7.1 - a. Give an example of a 33 matrix A with as many...Ch. 7.1 - Consider the coyotesroadrunner system discussed...Ch. 7.1 - Two interacting populations of hares and foxes can...Ch. 7.1 - Two interacting populations of coyotes and...Ch. 7.1 - Imagine that you are diabetic and have to pay...Ch. 7.1 - Three holy men (let’s call them Anselm, Benjamin,...Ch. 7.1 - Consider the growth of a lilac bush. The state of...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - For each of the matrices in Exercises 1 through...Ch. 7.2 - Consider a 44 matrix A=[BC0D] , where B, C, and D...Ch. 7.2 - Consider the matrix A=[1k11] , where k is an...Ch. 7.2 - Consider the matrix A=[abbc] , where a, b, and c...Ch. 7.2 - Consider the matrix A=[abba] , where a andb are...Ch. 7.2 - Consider the matrix A=[abba] , where a andb...Ch. 7.2 - True or false? If the determinant of a 22 matrix A...Ch. 7.2 - Ifa 22 matrix A has two distinct eigenvalues 1 and...Ch. 7.2 - Prove the part of Theorem 7.2.8 that concerns the...Ch. 7.2 - Consider an arbitrary nn matrix A. What is...Ch. 7.2 - Suppose matrix A is similar to B. What is the...Ch. 7.2 - Find all eigenvalues of the positive transition...Ch. 7.2 - Consider a positive transition matrix A=[abcd] ,...Ch. 7.2 - Based on your answers in Exercises 24 and 25,...Ch. 7.2 - a. Based on your answers in Exercises 24 and 25,...Ch. 7.2 - Consider the isolated Swiss town of Andelfingen,...Ch. 7.2 - Consider an nn matrix A such that the sum of the...Ch. 7.2 - In all parts of this problem, consider an nn...Ch. 7.2 - Consider a positive transition matrix A. Explain...Ch. 7.2 - Consider the matrix A=[010001k30] wherek is an...Ch. 7.2 - a. Find the characteristic polynomial of the...Ch. 7.2 - Prob. 34ECh. 7.2 - Give an example of a 44 matrix A without real...Ch. 7.2 - For an arbitrary positive integer n, give a...Ch. 7.2 - Prob. 37ECh. 7.2 - IfA isa 22 matrixwith trA=5 and detA=14 ,what are...Ch. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.2 - For which value of the constant k does the matrix...Ch. 7.2 - In all the parts of this problem, consider a...Ch. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.2 - Prob. 49ECh. 7.2 - Prob. 50ECh. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - Prob. 9ECh. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - Prob. 11ECh. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - Prob. 15ECh. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - For each of the matrices A in Exercises 1 through...Ch. 7.3 - Find a 22 matrix A for which E1=span[12] and...Ch. 7.3 - Find a 22 matrix A for which E7=2 .Ch. 7.3 - Find all eigenvalues and eigenvectors of A=[1101]...Ch. 7.3 - Find a 22 matrix A for which E1=span[21] is the...Ch. 7.3 - What can you say about the geometric multiplicity...Ch. 7.3 - Show that if a 66 matrix A has a negative...Ch. 7.3 - Consider a 22 matrix A. Suppose that trA=5 and...Ch. 7.3 - Consider the matrix Jn(k)=[000000000k10000k] (with...Ch. 7.3 - Consider a diagonal nn matrix A with rank A=rn ....Ch. 7.3 - Consider an upper triangular nn matrix A with aii0...Ch. 7.3 - Suppose there is an eigenbasis for a matrix A....Ch. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Suppose that B=S1AS for some nn matrices A, B, and...Ch. 7.3 - Is matrix [1203] similar to [3012] ?Ch. 7.3 - Is matrix [0153] similar to [1243] ?Ch. 7.3 - Consider a symmetric nn matrix A. Show that if ...Ch. 7.3 - Consider a rotation T(x)=Ax in 3 . (That is, A is...Ch. 7.3 - Consider a subspace V of n with dim(V)=m . a....Ch. 7.3 - For which values of constants a, b, and c are the...Ch. 7.3 - Prob. 41ECh. 7.3 - For which values of constants a, b, and c are the...Ch. 7.3 - Prob. 43ECh. 7.3 - For which values of constants a, b, and c are the...Ch. 7.3 - For which values of constants a, b, and c are the...Ch. 7.3 - Prob. 46ECh. 7.3 - For which values of constants a, b, and c are the...Ch. 7.3 - For which values of constants a, b, and c are the...Ch. 7.3 - Prob. 49ECh. 7.3 - For which values of constants a, b, and c are the...Ch. 7.3 - Prob. 51ECh. 7.3 - Find the characteristic polynomial of the nn...Ch. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Give an example of a 33 matrix A with nonzero...Ch. 7.3 - Prob. 56ECh. 7.4 - For the matrices A in Exercises 1 through 12, find...Ch. 7.4 - For the matrices A in Exercises 1 through 12, find...Ch. 7.4 - Prob. 3ECh. 7.4 - For the matrices A in Exercises 1 through 12, find...Ch. 7.4 - For the matrices A in Exercises 1 through 12, find...Ch. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - For the matrices A and the vectorsx0in Exercises...Ch. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - For the matrices A and the vectorsx0in Exercises...Ch. 7.4 - Prob. 19ECh. 7.4 - For the matrices A in Exercises 20 through 24,...Ch. 7.4 - For the matrices A in Exercises 20 through 24,...Ch. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - a. Sketch a phase portrait for the dynamical...Ch. 7.4 - Let x(t) and y(t) be the annual defense budgets of...Ch. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - In an unfortunate accident involving an Austrian...Ch. 7.4 - Prob. 35ECh. 7.4 - A machine contains the grid of wires shown in the...Ch. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - Find all the eigenvalues and “eigenvectors” of the...Ch. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Find all the eigenvalues and “eigenvectors” of the...Ch. 7.4 - Find all the eigenvalues and “eigenvectors” of the...Ch. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - Find all the eigenvalues and “eigenvectors” of the...Ch. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Find all the eigenvalues and “eigenvectors” of the...Ch. 7.4 - Prob. 52ECh. 7.4 - For a regular transition matrix A, prove the...Ch. 7.4 - Prob. 54ECh. 7.4 - Prob. 55ECh. 7.4 - Prob. 56ECh. 7.4 - Consider an mn matrix A and an nm matrix B. Using...Ch. 7.4 - Prob. 58ECh. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Prob. 61ECh. 7.4 - Prob. 62ECh. 7.4 - Consider the linear transformation T(f)=f from C...Ch. 7.4 - Prob. 64ECh. 7.4 - Prob. 65ECh. 7.4 - Prob. 66ECh. 7.4 - Consider a 55 matrix A with two distinct...Ch. 7.4 - Prob. 68ECh. 7.4 - We say that two n x n matrices A and B are...Ch. 7.4 - Prob. 70ECh. 7.4 - Prob. 71ECh. 7.4 - Prob. 72ECh. 7.4 - Prove the CayleyHamilton theorem, fA(A)=0 , for...Ch. 7.4 - Prob. 74ECh. 7.5 - Write the complex number z=33i in polar form.Ch. 7.5 - Find all complex numbers z such that z4=1 ....Ch. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - If z is a nonzero complex number in polar form,...Ch. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Prob. 9ECh. 7.5 - Prove the fundamental theorem of algebra for cubic...Ch. 7.5 - Prob. 11ECh. 7.5 - Consider a polynomial f() with real coefficients....Ch. 7.5 - For the matrices A listed in Exercises 13 through...Ch. 7.5 - For the matrices A listed in Exercises 13 through...Ch. 7.5 - For the matrices A listed in Exercises 13 through...Ch. 7.5 - For the matrices A listed in Exercises 13 through...Ch. 7.5 - For the matrices A listed in Exercises 13 through...Ch. 7.5 - Prob. 18ECh. 7.5 - Prob. 19ECh. 7.5 - Find all complex eigenvalues of the matrices in...Ch. 7.5 - Find all complex eigenvalues of the matrices in...Ch. 7.5 - Prob. 22ECh. 7.5 - Find all complex eigenvalues of the matrices in...Ch. 7.5 - Find all complex eigenvalues of the matrices in...Ch. 7.5 - Prob. 25ECh. 7.5 - Prob. 26ECh. 7.5 - Suppose a real 33 matrix A has only two distinct...Ch. 7.5 - Suppose a 33 matrix A has the real eigenvalue 2...Ch. 7.5 - Prob. 29ECh. 7.5 - a. If 2i is an eigenvalue of a real 22 matrix A,...Ch. 7.5 - Prob. 31ECh. 7.5 - Prob. 32ECh. 7.5 - Prob. 33ECh. 7.5 - Exercise 33 illustrates how you can use the powers...Ch. 7.5 - Demonstrate the formula trA=1+2+...+n . where the...Ch. 7.5 - In 1990, the population of the African country...Ch. 7.5 - Prob. 37ECh. 7.5 - Prob. 38ECh. 7.5 - Prob. 39ECh. 7.5 - Prob. 40ECh. 7.5 - Prob. 41ECh. 7.5 - Prob. 42ECh. 7.5 - Prob. 43ECh. 7.5 - Prob. 44ECh. 7.5 - Prob. 45ECh. 7.5 - Prob. 46ECh. 7.5 - Prob. 47ECh. 7.5 - Prob. 48ECh. 7.5 - Prob. 49ECh. 7.5 - Prob. 50ECh. 7.5 - Prob. 51ECh. 7.5 - Prob. 52ECh. 7.5 - Prob. 53ECh. 7.5 - Prob. 54ECh. 7.5 - Prob. 55ECh. 7.6 - For the matrices A in Exercises 1 through 10,...Ch. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Prob. 4ECh. 7.6 - For the matrices A in Exercises 1 through 10,...Ch. 7.6 - Prob. 6ECh. 7.6 - Prob. 7ECh. 7.6 - Prob. 8ECh. 7.6 - For the matrices A in Exercises 1 through 10,...Ch. 7.6 - Prob. 10ECh. 7.6 - Consider the matrices A in Exercises 11 through...Ch. 7.6 - Prob. 12ECh. 7.6 - Prob. 13ECh. 7.6 - Prob. 14ECh. 7.6 - Prob. 15ECh. 7.6 - Prob. 16ECh. 7.6 - For the matrices A in Exercises 17 through 24,...Ch. 7.6 - For the matrices A in Exercises 17 through 24,...Ch. 7.6 - Prob. 19ECh. 7.6 - For the matrices A in Exercises 17 through 24,...Ch. 7.6 - For the matrices A in Exercises 17 through 24,...Ch. 7.6 - For the matrices A in Exercises 17 through 24,...Ch. 7.6 - Prob. 23ECh. 7.6 - Prob. 24ECh. 7.6 - Prob. 25ECh. 7.6 - Prob. 26ECh. 7.6 - Prob. 27ECh. 7.6 - Prob. 28ECh. 7.6 - Consider an invertiblennmatrix A such that the...Ch. 7.6 - Prob. 30ECh. 7.6 - Prob. 31ECh. 7.6 - Prob. 32ECh. 7.6 - Prob. 33ECh. 7.6 - Consider a dynamical system x(t+1)=Ax(t) , whereA...Ch. 7.6 - Prob. 35ECh. 7.6 - Prob. 36ECh. 7.6 - Prob. 37ECh. 7.6 - Prob. 38ECh. 7.6 - Prob. 39ECh. 7.6 - Consider the matrix A=[pqrsqpsrrspqsrqp] , wherep,...Ch. 7.6 - Prob. 41ECh. 7.6 - Prob. 42ECh. 7 - If 0 is an eigenvalue of a matrix A, then detA=0 .Ch. 7 - Prob. 2ECh. 7 - Prob. 3ECh. 7 - Prob. 4ECh. 7 - The algebraic multiplicity of an eigenvalue cannot...Ch. 7 - Prob. 6ECh. 7 - Prob. 7ECh. 7 - Prob. 8ECh. 7 - There exists a diagonalizable 55 matrix with only...Ch. 7 - Prob. 10ECh. 7 - Prob. 11ECh. 7 - Prob. 12ECh. 7 - Prob. 13ECh. 7 - If Ais a noninvertible nn matrix, then the...Ch. 7 - If matrix A is diagonalizable, then its transpose...Ch. 7 - Prob. 16ECh. 7 - Prob. 17ECh. 7 - If A andB are nn matrices, if is an eigenvalue...Ch. 7 - Prob. 19ECh. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Prob. 28ECh. 7 - Prob. 29ECh. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - If a 44 matrix A is diagonalizable, then the...Ch. 7 - Prob. 33ECh. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - Prob. 36ECh. 7 - Prob. 37ECh. 7 - Prob. 38ECh. 7 - IfAisa22 matrixsuch that trA=1 and detA=6 , then A...Ch. 7 - If a matrix is diagonalizable, then the algebraic...Ch. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - Prob. 44ECh. 7 - Prob. 45ECh. 7 - Prob. 46ECh. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Prob. 51ECh. 7 - Prob. 52ECh. 7 - Prob. 53ECh. 7 - Prob. 54ECh. 7 - Prob. 55ECh. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Prob. 58E
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- 1 4 5 Question 3. Find A-1 (if exists), where A = -3 -1 -2 2 3 4 Question 4. State 4 equivalent conditions for a matrix A to be nonsingulararrow_forwardHow long is a guy wire reaching from the top of a 15-foot pole to a point on the ground 9-feet from the pole? Question content area bottom Part 1 The guy wire is exactly feet long. (Type an exact answer, using radicals as needed.) Part 2 The guy wire is approximatelyfeet long. (Round to the nearest thousandth.)arrow_forwardQuestion 6 Not yet answered Marked out of 5.00 Flag question = If (4,6,-11) and (-12,-16,4), = Compute the cross product vx w karrow_forward
- Consider the following vector field v^-> (x,y): v^->(x,y)=2yi−xj What is the magnitude of the vector v⃗ located in point (13,9)? [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places]arrow_forwardQuestion 4 Find the value of the first element for the first row of the inverse matrix of matrix B. 3 Not yet answered B = Marked out of 5.00 · (³ ;) Flag question 7 [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places] Answer:arrow_forwardQuestion 2 Not yet answered Multiply the following Matrices together: [77-4 A = 36 Marked out of -5 -5 5.00 B = 3 5 Flag question -6 -7 ABarrow_forward
- Assume {u1, U2, u3, u4} does not span R³. Select the best statement. A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set. B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³. C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set. D. {u1, U2, u3} cannot span R³. E. {U1, U2, u3} spans R³ if u̸4 is the zero vector. F. none of the abovearrow_forwardSelect the best statement. A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors are distinct. n B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0 excluded spans Rª. ○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n vectors. ○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors spans Rn. E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn. F. none of the abovearrow_forwardWhich of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.) ☐ A. { 7 4 3 13 -9 8 -17 7 ☐ B. 0 -8 3 ☐ C. 0 ☐ D. -5 ☐ E. 3 ☐ F. 4 THarrow_forward
- 3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forward(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0arrow_forwardFind the perimeter and areaarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Lecture 46: Eigenvalues & Eigenvectors; Author: IIT Kharagpur July 2018;https://www.youtube.com/watch?v=h5urBuE4Xhg;License: Standard YouTube License, CC-BY
What is an Eigenvector?; Author: LeiosOS;https://www.youtube.com/watch?v=ue3yoeZvt8E;License: Standard YouTube License, CC-BY