Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))
9th Edition
ISBN: 9780321962218
Author: Steven J. Leon
Publisher: PEARSON
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Chapter 2.3, Problem 14E
To determine
To calculate:The sent message of the matrix
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4 sinx cos2x+4 cos x sin2x-1=0
For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.)
6 -2
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A =
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P =
Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal.
P-1AP =
Chapter 2 Solutions
Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))
Ch. 2.1 - Let A=[324123232] (a) Find the value of...Ch. 2.1 - Use determinants to determine whether the...Ch. 2.1 - Evaluate the following determinants: (a) |3523|...Ch. 2.1 - Evaluate the following determinants by inspection:...Ch. 2.1 - Evaluate the following determinant. Write your...Ch. 2.1 - Find all values of for which the following...Ch. 2.1 - Let A be a 33 matrix with a11=0 and a210 . Show...Ch. 2.1 - Write out the details of the proof of Theorem...Ch. 2.1 - Prove that if a row or a column of an nn matrix A...Ch. 2.1 - Use mathematical induction to prove that if A is...
Ch. 2.1 - Let A and B be 22 matrics. a) Does...Ch. 2.1 - Let A and B be 22 matrices and let C=[ a 11 a 12 a...Ch. 2.1 - Let A be a symmetric tridiagonal matrix (ie., A is...Ch. 2.2 - Evaluate each of the following determinants by...Ch. 2.2 - Let A=[0123111122331223] (a) Use the elimination...Ch. 2.2 - For each of the following, compute the determinate...Ch. 2.2 - Find all possible choices of c that would make the...Ch. 2.2 - Let Abe an nn matrix and a scalar. Show that...Ch. 2.2 - Let A be a nonsingular matrix. Show that...Ch. 2.2 - Let A and B be 33 matrices with det(A)=4 and...Ch. 2.2 - Show that if E is an elementary matrix, then ET is...Ch. 2.2 - Let E1,E2 , and E3 be 33 elementary matrices of...Ch. 2.2 - Let A and B be row equivalent matrices, and...Ch. 2.2 - Let Abe an nn matrix. Is it possible for A2+I=O in...Ch. 2.2 - Consider the 33 Vandermonde matrix V=[1 x 1 x 1 21...Ch. 2.2 - Suppose that a 33 matrix A factors into a product...Ch. 2.2 - Let A and B be nn matrices. Prove that the product...Ch. 2.2 - Let A and B be nn matrices. Prove that if AB=I ,...Ch. 2.2 - A matrix A is said to be skew symmetric if AT=A ....Ch. 2.2 - Let A be a nonsingular nn matrix with a nonzero...Ch. 2.2 - Let A be a kk matrix and let B be an (nk)(nk)...Ch. 2.2 - Let A and B be kk matrics and let M=[OBAO] Show...Ch. 2.2 - Show that evaluating the determinant of an nn...Ch. 2.2 - Show that the elimination method of computing the...Ch. 2.3 - For each of the following, compute (i) det(A) ,...Ch. 2.3 - Use the Cramer’s rule to solve each of the...Ch. 2.3 - Given A=[121043122] determine the (2, 3) entry of...Ch. 2.3 - Let A be the matrix in Exercise 3. Compute the...Ch. 2.3 - Prob. 5ECh. 2.3 - If A is singular, what can you say about the...Ch. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Show that if A is nonsingular, then adj A is...Ch. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Let x, y, and z be vectors in R3 . Show each of...Ch. 2.3 - Let x and y be vectors in R3 and define the skew...Ch. 2 - Generate random 55 matrices with integer entries...Ch. 2 - Prob. 2ECh. 2 - Prob. 3ECh. 2 - Prob. 4ECh. 2 - Prob. 5ECh. 2 - Prob. 6ECh. 2 - Prob. 1CTACh. 2 - For each statement that follows, answer true if...Ch. 2 - For each statement that follows, answer true if...Ch. 2 - Prob. 4CTACh. 2 - Prob. 5CTACh. 2 - For each statement that follows, answer true if...Ch. 2 - For each statement that follows, answer true if...Ch. 2 - Prob. 8CTACh. 2 - Prob. 9CTACh. 2 - Prob. 10CTACh. 2 - Let A and B he 33 matrices with det(A)=4 and...Ch. 2 - Prob. 2CTBCh. 2 - Let A=[1111123413610141020] (a) Compute the LU...Ch. 2 - Prob. 4CTBCh. 2 - Prob. 5CTBCh. 2 - Prob. 6CTBCh. 2 - Let A be an nn matrix and let be a scalar. Show...Ch. 2 - Prob. 8CTBCh. 2 - Prob. 9CTBCh. 2 - Let A be a matrix with integer entries. If...
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- (e) Without using a membership table, show that (A N B) U (A N B) = A. State all the rules used.arrow_forwardThe function r has vertical asymptotes x =____________ (smaller value) and x = __________ (larger value)arrow_forwardProblem 1. 1.1. In each of the below, find a complete list of subgroups of the group G and write down their orders. a) The group G = Z/48Z b) The group G of rotations in D14. c) The group G = Z13 of 13-th roots of unity in C. 1.2. Find all elements x of the group G from 1.1 b) which generate G. 1.3. Let H = [[20]) ℃ Z/48Z. Using only order, determine which of the subgroups from your solution to 1.1 a) H coincides with.arrow_forward
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