Consider the following 2 x 2 matrix -5 A = 3. For any matrix, we have a clear understanding of some exponents: A" refers to multiplying a matrix to itself n times and A-l refers to the inverse matrix. Combining this idea gives A- = (A-')", the nth power of the inverse. A natural question to ask is, can we take the nth root of a matrix? We're going to try to find A/3, i.e. a matrix that when we cube it gives A. (a) Calculate the eigenvalues and eigenvectors of A. (b) Find a matrix P and a diagonal matrix D such that A = PDP-1. (c) Find a matrix E such that E = D. Explain why this result is simple compared to finding the cube root of A.

Consider the following 2 x 2 matrix -5 A = 3. For any matrix, we have a clear understanding of some exponents: A" refers to multiplying a matrix to itself n times and A-l refers to the inverse matrix. Combining this idea gives A- = (A-')", the nth power of the inverse. A natural question to ask is, can we take the nth root of a matrix? We're going to try to find A/3, i.e. a matrix that when we cube it gives A. (a) Calculate the eigenvalues and eigenvectors of A. (b) Find a matrix P and a diagonal matrix D such that A = PDP-1. (c) Find a matrix E such that E = D. Explain why this result is simple compared to finding the cube root of A.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Solve the matrix

A: we will solve such that we can get the solution to system of linear equations

Q: 6. Use the given information to find 'A'. 21 (I + 24)¯ = 4

A: 6. Given, I+2A-1=-1245 Let B=-1245 Now this can be done as follows:…

Q: \o _ 0 0 1|-9 -1 6 -7/ \o _ 0 0 1-9 -1 6 -7/ -3 0 2 -2 -1 1 A-1 1 1 1 -- 2 -9 -1 6 -7

Q: explain why the following matrix does not have an inverse A=√125 352

Q: ✓ 1.6 Each pair of matrices differ by one row operation. Use this operation to compare det(A) with…

Q: For the following matrix, do a single valid elementary row operation to get a 1 in row 1, column 1.…

Q: b. If c # 0, is the following property true or false?· (CA)-1 = c-1A-1

A: 4 Given Aand B are the n×n invertible matrices. b If c≠0 then we have to check whether the property…

Q: Q5/ By Using Cayley-Hamilton method the inverse of the following matrix is:

Q: Ouestoon = Find the inverse of the matrix with A'= Adj A A= -2

A: The objective is to find inverse of the given matrix using the given formula Given:

Q: For the following matrices (or vectors) are given in Cartesian coordinates: 1½/21 A = [-4 3]…

Q: In the context of a 3 x 4 matrix, write down elementary matrices for the following operations: (a)…

Q: 1 -5 0 0 | -2 1 0 0 7 5 | -5 0 1 0 | 3 j. 0 1 -4 -3 2 0 | 7 0 0 1 6 -2 | 4 0 0 0 | 1 0 0 6 | -5 1 -5…

Q: MATRIX A: 4 -3 5 -11 9 8 -5 6 7 1 MATRIX B: -11 9 10 -5 3 MATRIX C: 0 4 -82 -48 -5 0 -2 0 0 0 -9 15…

Q: (b) Table Q4(b) is generated from the function ƒ(x)= e* - 4x² + B , where B is the last two digits…

A: Given: fx=ex-4x2+B To find: f'1.5

Q: Consider the matrix in the image (i) Determine the inverse matrix B^−1 , of B. (ii) Using the…

Q: Write the 4 x 4 elementary matrix which accomplishes the row operation R3 - 5 R2 ---> R3 when you…

A: let I be the 4×4 identity matrix I=1000010000100001

Q: Question -x1 + 3x₂ = 2 2x₁ + x₂ + 4x3 = 3 x2 + 2x3 = 4 [A-¹|I], Find A-¹. (a) Using [IA] (b) Find…

Q: For Square Matrix A, B of the same size is it true (A + B)-1 = A-1 + B-l? Explain

Q: 10 Let A = -2 1 B (Enter a matrix like -3 -6 -87 Find the product of any two of the matrices. The…

A: The rule of order (or dimension) of matrices for matrix multiplication is as follows:For two…

Q: For each of the matrices below, determine whether it is RREF. • If yes, copy the matrix on the…

A: A matrix is in RREF if it meets all of the following conditions: If there is a row where every…

Q: Solve for the matrix X: 35 1 2 *(²2)- ²×(²3)-( :) X = 72 20 The first row of X is given by is X11 =…

Q: If A and B are 2 × 2 matrices, det (A) = 1, det(B) = 4, then det (AB) = 4 det (-2A): det (A¹) = 1…

A: If A and B are 2*2 matrices, det(A) = 1, det(B)= 4, then Find det(-2A).

Q: Homework : Find the inverse of the matrix and verify that A-'A = A A-1 = 1,

Q: Suppose the trace of a matrix is equal to 10. If this matrix is also an identity matrix, how many…

A: Given: The trace of a matrix is equal to 10 and the matrix is an identity matrix. To determine:…

Q: 1. True or False: (Matrix [mxn]) [3x6][5x3]=[5x6] O True O False O Maybe

Q: he matrix is Α = et result hitting · 230 1 -1 3 401 -1 Α Α ΑΑ

A: Topic:- matrix algebra

Q: en the definition tr rices (no numbers). (d) = a + d show that tr(A B) = tr(BA) using gen

Q: Determine the matrix A x 1, if A=(13) and 1=(9)=

A: Given A=-1043, I=1001 To determine: the matrix A×I

Q: Could a 4 by 4 matrix A be invertible if every row contains the numbers 0, 1, 2, 3 in some order?…

A: We know that a 4×4 matrix has four rows and four columns. A matrix is said to be invertible if the…

Q: Use the of a the inverse Possible. w/or O matrix capabilities calculator to find the matrix, of 2…

A: Find the inverse of the given matrix.

Q: To divide the LHS by a matrix on the RHS, what steps do you follow?

A: To find: To divide the LHS by a matrix on the RHS, what steps do you follow?

Q: The equation A² - 2A + I = O implies that ---Select--- Need Help? Read It ✓. It follows that…

Q: Solve the following: 3 1 a. Find the inverse matrix (A") if the matrix A = -1 -4 3

Question

100%

Consider the following 2 x 2 matrix
A =
For any matrix, we have a clear understanding of some exponents: A" refers to multiplying a matrix to
itself n times and A-l refers to the inverse matrix. Combining this idea gives A-n = (A-!)", the nth
power of the inverse.
A natural question to ask is, can we take the nth root of a matrix? We're going to try to find A/3, i.e. a
matrix that when we cube it gives A.
(a) Calculate the eigenvalues and eigenvectors of A.
(b) Find a matrix P and a diagonal matrix D such that A = PDP-1.
(c) Find a matrix E such that E = D. Explain why this result is simple compared to finding the cube
root of A.
(d) Using part (c), find a matrix B such that B3 = A.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Trending now

This is a popular solution!

Step by step

Solved in 8 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Inverse of a Matrix$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Answer both otherwise don't solve.
Multiply the matrices:
b) A civil engineering firm plans to sign a contract with a customer. The contract calls for the construction of two office buildings which are denoted as Building X and Building Y. According to estimates derived in the preliminary design phase, the firm knows that the total cost of the project will be $50,000,000. It is also known that Building X will cost $5,000,000 more to construct than Building Y. Use matrices' inverse to find the cost of each building. an
Please solve max 20-25 minutes about chapter Linear Algebra thank u
Here matrix A 4 2- i 9. A= |2+i 0 3+i 3- i 9 7 Can you solve for A· A"(Transpose matrix)?
do Q1 2 ONLY
Help me
how can I develop 3x3 matrix to 4x4 matrix as in the picture, would you explain it
Show that if A is square matrix that satisfies the equation 2 A² - A - I = O, then its inverse is A-¹ = 2 A-I. The equation 24² - A - I = O implies that ---Select--- ✓. It follows that ---Select--- ✓. Notice the last equation means that ---Select--- multiplied with A is the identity, which is what we wanted to prove.
How do you calculate when the matrix is equal to 0 ?