11 -12 8. -6 12 -14 10 -8 A = -5 6. -3 3 -14 18 -12 11 Find a matrix P such that D = P-l AP is the Jordan canonical form of A. The Jordan form is upper triangular. The blocks are ordered increasingly by eigenvalue and then by block size. 3 1.5 1 3 1 2/3 -0.5 1 P = D = -1.5 -3 1 2

11 -12 8. -6 12 -14 10 -8 A = -5 6. -3 3 -14 18 -12 11 Find a matrix P such that D = P-l AP is the Jordan canonical form of A. The Jordan form is upper triangular. The blocks are ordered increasingly by eigenvalue and then by block size. 3 1.5 1 3 1 2/3 -0.5 1 P = D = -1.5 -3 1 2

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: Find eigenvalue, and eizenvectors of the matrix - 14 12 1 - 20 17

A: The given matrix is -1412-2017 We have to find the eigenvalues and corresponding eigenvectors of…

Q: —2 2 6 -2 -4 C = 1 [−1 1 has two distinct eigenvalues with X₁ < λ₂. The smaller eigenvalue ₁ : = has…

A: Here given matrix as C=-2261-2-4-113

Q: the matrix has two eigen vector one of (ارفق الاجابة)this N|HN|W 0 1 2 0 }] -1 0 12032

Q: Use the table or a calculator to find the final accumulated amount and the total interest. (Round…

A: Use the table or a calculator to find the final accumulated amount and the total interest. (Round…

Q: 5 The matrix A= -2 7 0 has eigenvalues A₁ = 2 and A₂ = 3. An eigenvector for 2 is = 2 1 -2 3 [-2 10…

A: (.) Given matrix is, Matrix has eigen values and . An eigen vector for is and has…

Q: Find a basis {b₁,b2,...} for the eigenspace corresponding to (the eigenvalue) X. -15 -32 -18 12 -56…

Q: [-4 2 -2 Suppose B = 2 -7 4. -2 4 -7 a. Compute orthonormal bases for the eigenspaces of B. b. Use…

Q: The matrix The larger eigenvalue X₂ - Is the matrix A defective? A = choose has two real eigenvalues…

Q: -4 2 Given: A = 2 -7 4 has eigenvalues -3 and – 12. [-2 4 -7 a) Explain why we know that A is…

A: Given the matrix A=-42-22-74-24-7 has eigenvalues -3 and -12. (b) We will find an orthogonal matrix…

Q: X= 2 is an eigenvalue of each matrix below. Match each matrix with the correct pair (algebraic…

Q: matrix

Q: Diagonalize A the matrix A. -27 2 3 4 3+ i√5 0 0 [S+W³² $ "VE] [3+1 0 3-i√√5 i√5] 0 0 [-³+1 0 O…

Q: 2. The eigenvalues 31 Let A =-2 6 4 2 and corresponding eigenspaces are: -1 2 = 7: 1 and 1 = -2: 1/2…

A: Given,

Q: Consider the matrix -2 A=1 2 1 0 0 0 1 3 Q1.. Find the eigenvalues of the matrix A. Q2. Find the…

A: Eigen values of a matrix A=00-2121103 is given by det A-λI=0 -λ0-212-λ1103-λ=0 Evaluating the…

Q: For the given matrix A, find a basis for the corresponding eigenspace for the given eigenvalue. 19…

Q: 3 log(x^4)-2 log(3x) write as a single logarithm with a coefficient of 1

Q: 5. Consider a linear transformation T R-R2 which reflects a vector about the line y=-r, and dilates…

A: Consider the given information:

Q: Show justifying that if A and B are square matrixes that are invertible of order n, A-¹BA then the…

Q: 3 0 0 -2 2. Find h in the matrix A = 7 such that the eigenspace for å= 7 is one- -1 0 5 7 4 -6…

A: Given the matrix is A=3000-27000h-104-657. The matrix has an eigenvalue λ=7.

Q: Select an Answer v 1. 1 4 -8 2 2 7 -12 2 A = , 1 = -1 0 4 -7 0 4 -4 -1 2.

A: As per our guidelines we are supposed to answer only ? 3 sub- parts ( if there are multiple sub-…

Q: Which of the following is not an eigenvalue of the matrix -V5 V5 1 2 -13 -1 V3 -V5 5i -5i They are…

Question

11
-12
8
-6
12
-14
10
-8
A =
-5
6.
-3
-14
18
-12
11
Find a matrix P such that D = P¯' AP is the Jordan canonical form of A. The Jordan form is upper triangular. The blocks are ordered increasingly by
eigenvalue and then by block size.
3
1.5
1
1
1
2/3
-0.5
1
P =
D =
-1.5
1
-3
1
2

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Eigenvalues and Eigenvectors$

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

| The matrix 4 A = -3 7 12 -6 -11 has eigenvalues -5,1, and 4. Find its eigenvectors. The eigenvalue -5 has associated eigenvector The eigenvalue 1 has associated eigenvector The eigenvalue 4 has associated eigenvector
5. Help me with P
The matrix 8 -24 -68 C = 28 70 2 -12 -30 has two distinct eigenvalues with A,
8 1 act on C2. Find the eigenvalues and a basis for each eigenspace in C2. Let the matrix - 10 2 Select all that apply. - 3+ 3- A. A= 1-5i; V= B. A= -5+ i; v= 10 -3+ i 3-i O c. A= 5+ iv = O D. A=5+ i; v = 5 10 -3- i -3+ O E. A=5- i; v= O F. A= -5- i v= - 3- i O G. A=1+5 i; v= O H. A=5- i; v= 10 10
1 Given that A is a 3 x 3 matrix with eigen pairs (-9, -2 5 3 (12, -2). Find the matrix B = M-¹AM where M = b₁1 b12 b13 . Let B = b22 b23 then b32 b33 b11 = , b13 = b21 b31 || b21 b31 , b12 , " = b22 = b32 = = , b23 = , b33 (1, 4 3 -1 4 3 and -1 3 1 -2 -2 1 5
5 Find the specified change-of-coordinates matrix. 7) Let B and C be bases for R2, where Find the change-of-coordinates matrix from B to C. b1 = ¹₁ -[3]- ¹₂ -[-+-C₁ -[3]· <₂2-[-₁6] b2 = C1 = C2 =
Determine if v is an eigenvector of the matrix A. 6 -1 Select an Answer Select an Answer Select an Answer ✓ 1. A 2. A = 3. A = - 5 2 1 1 -5 -6 3 0 0 -2 -1 -6 1 1 1 0 1 1 1 % 0 0 -8 - 0 0 3 -3 -5 7 -3 5 10 2 10 9 -2 13 0 -5 -5 0 0 9 。 9 V = = V = -2 2
Determine if å is an eigenvalue of the matrix A. Select an Answer + 1. 7 -2 -14 4 -2 -1 8. -6 6 -2 -11 2 A = ,2 = -6 6 -2 -14 5 Select an Answer 2. 2 3 0 14 -2 -1 2 -4 1 3 1 11 A = ,2 = -7 0 0 0 -2 Select an Answer 3. 1 0 0 0 0 1 -1 -1 2 0 2 A = , λ-2 -2 0 0 -1
MATRIX A Is axa T ElbEN VALUES ARG -3 AND a FWD CHE EIGEN. VALUES Aa A+3I IS THIS
ht) The matrix -5 10 -5 10 0 -5 10 has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace. The eigenvalue ₁ is The eigenvalue 2₂ is 0 A = 0 and a basis for its associated eigenspace is and a basis for its associated eigenspace is
4. Consider the following matrix: 3. -2 A =-14 15 18 -18 -10 (a) Find the eigenvalues of A. (b) Find three linearly independent eigenvectors for A and state the algebraic and geometric multiplicity for each eigenvalue. Form a matrix C whose columns are the three linearly independent eigenvectors that you found in (b). Verify that C-1 AC is a diagonal matrix (which we call D). (d) Use your previous answer to find a matrix B with the property that B3 = A. (e) For any real matrix A, write down a sufficient condition for a real matrix E to exist such that E2 = A, and prove that this condition is sufficient. %3D
Determine if vv is an eigenvector of the matrix AA.