Suppose the matrix, $ A $, has eigenvectors \[\begin{bmatrix} 3 \\ 0 \\ -2 \end{bmatrix},\begin{bmatrix} 2 \\ 1 \\ -2 \end{bmatrix},\begin{bmatrix} 5 \\ 0 \\ -3 \end{bmatrix}\]whose eigenvalues are 8, $-2$ and 4 respectively. Then, using the same order, $ A $ can be written in the form \[A = P \Lambda P^{-1}\]where\[P = \begin{bmatrix} \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \end{bmatrix}\]and\[\Lambda = \begin{bmatrix} \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \end{bmatrix}\]

Given: The matrix A has eigenvectors 30-2, 21-2 and 50-3 whose eigenvalues are 8, -2 and 4…

Answered: 3 2 Suppose the matrix, A, has…

3 2 Suppose the matrix, A, has eigenvectors and whose eigenvalues are 8, – 2 and 4 respectively. Then, using the same order, A can be written in the form A = PAP-1 where P = and 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: a) Determine the eigenvalues and eigenvectors of the following matrix. 3 -2 1 2 -4 3 l16 -4 1

A: Given matrix is 3-212-4316-41xyz=λxyz ∴A=3-212-4316-41 The characteristic equation of A is…

Q: Q2A)Matrix A = [1 2. ,find Eigen values of A².

A: The given matrix is A=1342 To find: the eigenvalues of A2

Q: A real 4x4 matrix A satisfies A? = I , where I is the identity matrix. The positive eigenvalue of A…

A: To find: The eigen values of matrix A. Given: The matrix A having dimension and satisfies .…

Q: Q2\ Find the Eigen values of matrix A? [1 -1 01 A= 0 2 [2 1]

Q: Determine the eigenvector associated with = 3 for the matrix h 6 2-2 25 0 - 2 0 7

Q: Suppose the matrix, A, has eigenvectors 00-0 respectively. Use this order of eigenvectors to find…

A: It is provided that the eigenvectors of A are 101, 011, 201 and the corresponding eigenvalues are…

Q: A = -53 -70 35 45

Q: F be eigenvectors of the matrix A which correspond to the eigenvalues A₁ = -3 and X = 2,…

Q: For a matrix M, Mv = \v, evaluate = (Mv)iv in two different ways to find a condition on the…

A: Follow step 2nd.

Q: A be an orthogonal n by n real matrix where n is an odd number. Show that 1 or -1 must be an…

Q: 3. The characteristic polynomial of the matrix A = -1 -1 -1 -1 4 -1 is (A-2)(X - 5)². -1 4 a) Find…

Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save…

A: As given eigenvalues are 10,10,1. So eigenvectors are given by, A-λIV=0 where V is the eigenvector…

Q: Find a 2 x 2 matrix with no zero entries that have eigenvalues 3 and 13. (Enter each matrix in the…

Q: Suppose ?<0λ<0 and ?u are a pair of eigenvalue and eigenvector of a 2×22×2 matrix ?A and ?=??v=Au.…

Q: Let A be 2 x2 matrix. if trace A 8 and det(A)= 12 then the eigenvalues of A are Select one: a. 3,4…

A: Result : If A is a 2×2 matrix, then it's characteristic equation is given by x2 - (tr A) x + (det…

Q: If A is 3 x3 matrix with eigenvalues A= 4,4,3 , then A is defective. Select one: O True O False

A: We have given a matrix A . A is 3×3 Eigenvalues λ= 4,4,3. Here λ=4 is eigenvalue of multiplicity 2.…

Q: 3 -5 Find the eigenvalues of the matrix A 1 10 = Choose File No file chosen Enter both values…

Q: Let A be a 3 x 3 matrix with eigenvalues 7/2, 7//4, 7/8. If the eigenvalues of A- are A1,2, 13, then…

A: we have given eigen values of matrix A these are 7/2,7/4,/7/8 As we know eigen value of A-1 =1/lemda…

Q: Find a 3 x 3 matrix A that has eigenvalues λ = 0, 12, -12, with corresponding eigenvectors 400…

A: We have to find a matrix that has eigenvalues , with the corresponding eigenvectorsWe know thatIf A…

Q: A [11 -2] 50-5 Find the eigenvectors of the given matrix: 181-18) 12 i

Q: Diagonalize the matrix A = -1 3-4 -2 3-4 1 1 3 Verify that AS = SA. Note that the some of the…

Q: Suppose B = XAX2, where X is the eigenvector matrix of B and A is its eigenvalue matrix. Compute the…

A: Please check step 2 for the solution.!

Q: Let A be 2 x 2 matrix. if trace A =8 and det(A)= 12 then the eigenvalues of A are: Select one: a.…

A: Characteristic equation of matrix A is given by λ2-trAλ+detA=0 where λ denote the eigenvalues ,…

Q: If A is 3 x 3 matrix with eigenvalues 0, 2, 3. Then: | a. |AA"| = 0 а. O b. |AA"|= 6 %3D c. |AA"| =…

A: See solution below.

Q: Suppose A is a 4X3 matrix whose elements are all 1's. What are the eigenvalu- Select one: O a. (3,…

A: Suppose A is 4×3 matrix whose elements are all 1's. What is the eigenvalues of AAT?

Q: 3 Let v₁ = -3 and v2 = 2 be eigenvectors of the matrix A which correspond to the eigenvalues X1 1 0…

Q: A 2x2 matrix is known to have the eigenvalues -3 and 4. What are the eigenvalues of the following…

A: We will find out the required value.

Q: Using your q-1 and p-3, find the eigenvalues of the matrix

Q: Suppose A is a 2 × 2 matrix. Use the characteristic equation to show that A and A¹ have the same…

A: We have to show that have same eigenvalues using given data.Concept required:Eigenvalues of are…

Q: Find the eigenvalues and eigenvectors of the matrix A = 181 A₁6i, V₁ = and X₂ -6i, 32 = -6 97 -8 6

A: The given matrix is; A=[-6 9 -8 6]

Q: 04) Find the eigenvalues and eigenvectors of the following matrix and liagonalize it if possible. 7…

A: Given : 3x3 matrix is given 7 0 -3 -9 -2 3 10 0 -8

Q: Give an example of a matrix A with the order 2x2 along with two vectors a and b, with terms a is an…

A: Use simple matrix theory of eigenvalues to come up with this example

Question

100%

Suppose the matrix, $ A $, has eigenvectors

\[
\begin{bmatrix}
3 \\
0 \\
-2
\end{bmatrix},
\begin{bmatrix}
2 \\
1 \\
-2
\end{bmatrix},
\begin{bmatrix}
5 \\
0 \\
-3
\end{bmatrix}
\]

whose eigenvalues are 8, $-2$ and 4 respectively. Then, using the same order, $ A $ can be written in the form

\[
A = P \Lambda P^{-1}
\]

where

\[
P =
\begin{bmatrix}
\boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{}
\end{bmatrix}
\]

and

\[
\Lambda =
\begin{bmatrix}
\boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{} \\
\boxed{} & \boxed{} & \boxed{}
\end{bmatrix}
\]

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

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

Let -3" -2,03= be eigenvectors of the matrix A which correspond to the eigenvalues X1 =-4, X2= -1, and X3 = 3, respectively, and let エ= Express i as a linear combination of v1, v2, and vz, and find A. Az =
Find the eigenvalues and eigenvectors of: 3 1 and state whether the matrix is singular or nonsingular.
Help me
Let A be 2 x2 matrix. if trace A =8 and det(A)= 12 then the eigenvalues of A are: Select one: a. 4,4 b. 10,2 C. 3,4 d. 2,6
use Equation in the picture to verify that λ and v are an eigenvalue/eigenvector pair for the given matrix A.
Consider a matrix Xrxn, the two eigenvalues of the matrix are 6 and 10 + v-1). If n is equal to three then what is the trace of X?
Help with b please
Consider the matrix A =−6 4−2 0 A) Determine the eigenvalues of the matrix A B) For each eigenvalue from part (A), determine the corresponding eigenvectors of the matrix A. Use row operation notation to indicate steps
Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are 10 and -9. A = 1 -3 9 -3 93 9 3 1 Enter the matrices P and D below. (Use a comma to separate answers as needed. Type exact answers, using radicals as needed. Do not label the matrices.)
Find all the eigenvalues and eigenvectors of the given matrix. ( ) -2 4 -1 Number of distinct eigenvalues: 1 Choose one 1 1 ( ) (1) ? ||
Determine if v is an eigenvector of the matrix A. Select an Answer ✓ 1. -3 -4 -E-D] = 20 15 A = Select an Answer A = Select an Answer 10 -2 -RED V= 3 5 A = 7 -4 2. 6 -3 3. 3 , V = 3 -1 -1 6 [9] 2
Need only a handwritten solution only (not a typed one).