For the following matrices A, compute A is a 3x3 matrix, having eigenvalues -12-2,and-4. A= -3.8 1-4 -1.6 -28 04 -0.8 0.4 -3.6 Find their corresponding eigen vectors V₁, V₂, V3 Defined by matrix Let V=/V₁ V₂ V₂ => (**) example V ₁AV = (-100 مانا- 0-20 00-4/ A=VrV¹ eft = Vent vi VI O C²² 00 e-ut

For the following matrices A, compute A is a 3x3 matrix, having eigenvalues -12-2,and-4. A= -3.8 1-4 -1.6 -28 04 -0.8 0.4 -3.6 Find their corresponding eigen vectors V₁, V₂, V3 Defined by matrix Let V=/V₁ V₂ V₂ => (**) example V ₁AV = (-100 مانا- 0-20 00-4/ A=VrV¹ eft = Vent vi VI O C²² 00 e-ut

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Compute eigenvalues and eigenvectors for the matrix A and i power of 2 -13 7 A= A-[2²8] 4²-[23³] = 6…

A: Given matrix is A = -1320, A2 = 7-3-26

Q: The matrix has eigenvalue X = -2 repeated three times. Find an -2-eigenvector for A: v= Give a…

A: Consider matrix Applying Then becomes Then can be written as

Q: Suppose the 3 × 3 matrix A has eigenvalues λ1 = −6, λ2 = −2, and λ3 = 5.

A: according to guidelines we can solved only first 3 subparts thank you We have the eigen values of…

Q: 10. It is known that matrix A 4x4 has the following eigenvalues: 2, =-2, 2, = 1, z =-1, 24 = 2.…

Q: 21.1f A' = 34² where A is n by n matrix, then (a) A= 31 (b) A 31 if rank((A) =n () A" =!1 (d) a and…

Q: symmetric matrix and A1 and alues of the matrix. The 2 1 gen vector is 2 and 1

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: 7.) For matrix A, find (if possible) a nonsingular matrix P such that P-'AP is diagonal. Verify that…

Q: Given the matrix and its eigenvalues 3- 1-R 1 becomes has eigenvalues R = 1 + i -1 1-R Find the new…

Q: Construct a symmetric matrix A with eigenvalues A1 = -3 and A2 = 10 and corresponding orthogonal…

Q: - find the eigenvectors of the diagonal matrix (Â) J where. 2 5 0-12 2 4 10 A = and P=["} 1 2 5 4 O…

Q: For the following matrix [40 0 0 0 2 0 0 00-1 0 Loo 0 -2. In your answer, use 3 significant digits…

A: Please see the below picture for detailed solution.

Q: The eigenvalues of a 3x3 matrix A are -4,2,9. Find the determinant of (A-1)T

Q: (e) Show that the matrix is diagonalizable and find an invertible matrix P and a diagonal matrix D…

Q: 2. For the matrix (i) Find all eigenvalues, t.

A: Introduction: Let A be an n×n square matrix.If a NONZERO vector x∈Rn and a scalar fulfill Ax =λ x,…

Q: Diaganolize the following matrix such that: D=(P^T)(A)(P). Rather than finding the inverse matrix,…

Q: What is the eigenvectors of the matrix 64 A = O None of the others

Q: For the matrix A, find (if possible) a nonsingular matrixP such that P-AP is diagonal. (If not…

Q: If the diagonal matrix that is congruent to the given matrix is 2 0 0 0 -1 0 0 0 0 Can we…

A: Given matrix is A=−101011011. And the diagonal matrix that is congruent to the given matrix A is…

Q: 1 A = -1 P = Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal. p-1AP…

Q: One of the eigenvalues of Matrix A is 2. If we add to Matrix A a diagonal matrix with diagonal

Q: Let A = [ - (a) Find eigenvalues and corresponding eigenvectors. (b) Find a nonsingular matrix P…

A: Since there are multiple subparts the first three subparts is answered.Kindly repost with the…

Q: Choose the 2 by 2 nondiagonal matrix such that its eigenvalues are different positive numbers…

A: We first write a 2×2 non diagonal matrix whose eigen values are different positive numbers then we…

Q: ). -18 -7 A = 3 ( 8 11 = -1 og 12 = 2. %3D

Q: True of false If one of the eigenvalues of a matrix has a multiplicity of 2, then two eigenvectors…

Q: Find a 3 x 3 matrix • The vectors V₁ = satisfying the following properties: • A has two eigenvalues:…

A: The given problem is to find the matrix A for which the given eigenvalues and corresponding…

Q: Assume that a 3 x 3 matrix A has eigenvalues 21 = 1,22=0.8, 23=0.6 With corresponding eigenvectors…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: Find a 3 x 3 matrix A whose -4-eigenspace is and whose 3-eigenspace is A = V = {(x, y, z) in R³ |…

A: To Find: a 3×3 matrix whose 4-eigenspace is V=x, y, z in ℝ3 | -8x-14y+10z=0 and whose 3-eigenspace…

Q: Q2) for the following Matrix 'A', Please determine the following: A = a. Eigenvalue of A b.…

Q: wo eigenvalue If n is equal

Q: For a rectangular matrix A, how are the eigenvalues of ATA and AAT related?

A: For a rectangular matrix, the number of rows is equal to the number of columns. The transpose matrix…

Q: 3 6 -3 -1 -2 1 2 4 -2

Question

For the following matrices A, compute At
A is a 3x3 matrix, having eigenvalues
-12-2, and-4-
A=
1-3-8
1-4 -1.6
-28
0.4
-0.8 0-4 -3.6
Find their corresponding eigen vectors
V₁, V₂, V3
مانا -
Defined by matrix > Let V=/V₁ V₂ V3
(5)
example,
V ₁AV = (-100
0-20
00-4/
A=VrV¹
eft = Vent vi
At
v/et
o eat
e-4t,

Expert Solution

Step 1

Step by step

Solved in 4 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

It's unclear to me how the eigenvectors were calculated.
And the final value of e^Atis also unclear to me..

Step 2
eigen vector are
eat
1- ^ 76² ^ = 702
veît
(using
é
Calculated incorrect.
-2.8
-2-8
-0.8
eigenvector corresponding to a = -1 be m
[:]
e-2t
[
1.५ -1.6
1.4
-1.6
-2.6
0.4
Row- reduction
[²
-1/₂
m=
thia
-1.8 1.4
JJ
0.4
-0.8
1.4
0=Eul
7/1. = 11e
[:]
O
eigenvector corresponding to a = = 2 ben
lue
)
-1.6
ES-BO [:]
- २.४ 24
-1.6
-1.6
m₂
[618]
m3
Eut
Let m₂ = 1
n2
из
[8] - [%]

let n₂ = 1
₂ = -4
31=-4
[=4
Similarly eigenvector corresponding 2 = -4 be p
P = [ 1 ]
V =
VA
=
Adjv
12
det V
=
O
Adj V
det V =
vy
V
=
Adj V
A
-5
1
51/2-1/2
1/2₂
9
det V = 5/2
-1
1/2 (-5)
2
-5
1
T
5
1/2
-1/₂
1/2
+4+1
50
1/2 1/2
-1/2 2
2 2
-2/5 1/5 1/5
215
-1/5 4/5

Solution

by Bartleby Expert

SEE SOLUTION

Follow-up Question

Compute e^At

Solution

by Bartleby Expert

SEE SOLUTION

Follow-up Question

There was a compete e^AT part

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

For the matrix A , there is an invertible matrix P such that P^(−1)*AP = D, where D is a diagonal matrix with the eigenvalues of A on the diagonal. Calculate the matrix product P^(-1)*AP
= - 1. Then the a12 = a,1 = + 1 and a,, = - = + 1 and a22 a21 5 Let A be the 2 x 2 matrix with elements a,, eigenvalues of the matrix A19 are
A 2x2 matrix has trace -13. One of its eigenvalues is -9. What is the other eigenvalue?
4 A be the 2 x 2 matrix with elements a11 a12 = +1 and a22 = -1. Then the eigenvalues of the matrix A19
(6) Let Q1 be an m x n matrix with orthonormal columns and Q2 be an n x p matrix with orthonormal columns. Show that Q1Q2 has orthonormal columns.
A) Find the eigenbasis of the matrix and diagonalize it (if possible): when p=4. Also, Use this diagonalization to find A^3 and A^7. (the matrix in the photo) B) For the matrix in part (A), find A^2 and A^1 theorem.using Cayley-Hamilton
If A is a 3 x 3 matrix with Eigen values, x, y, z then the Eigen values of A'are 1 1 1 (a) y.z (b) -х, -у,-2 (с) (d) x. y.z
Determine if v is an eigenvector of the matrix A