Answered: Verify that λ, is an eigenvalue of A… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 75E

See similar textbooks

Related questions

Question

help please. 7

Verify that λ, is an eigenvalue of A and that x; is a corresponding eigenvector.
2₁ = 8, X₁ (1, 0, 0)
λ₂ = 6, x₂ = (1, 2, 0)
= (-4, 1, 1)
23 = 7, X3
AX1
A =
8 -1
O 00
AX3
=
0
8 -1 5 1
-⠀⠀
= 0 61 0 =
0 07 0
0 07
8 1 5
1
-D
AX₂=
0 6 1 2 =
0 07 0
6
5
1 17
8 -1 5
6 1
07
↓ 1
↓ 1
=
→
= 6
1
-4
=
-#10
0
NH
1
0
= 2₁x1
= 2₂x2
= 7 1=13*3

Expert Solution

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Determine all nn symmetric matrices that have 0 as their only eigenvalue.
Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. = 13, x1 12 = -3, x, = (-2, 1 0) 13 = -3, x3 = (3, 0, 1) -1 4 -6 (1, 2, –1) A = 4 5 -12 -2 -4 -1 4 -6 1 1 = 13 2 = 1,x1 4 5 -12 = -2 -4 3 -1 -1 -1 4 -6 -2 -2 AX2 1 = 12x2 4 5 -12 1 = -2 -4 -1 4 -6 3 3 AX3 = 13x3 4 5 -12 -3 = -2 -4 1
Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 1 = 5, x, = (1, 2, -1) 12 = -3, x, = (-2, 1 0) 23 = -3, x3 = (3, 0, 1) -2 2 -3 A = 2 -6 -1 -2 -2 2 -3 Ax = 1 -6 = 5 = -1 -2 -1 -1 -2 2 -3 -2 -2 Ax, = 1 -6 = -3 -1 -2 -2 2 -3 Ax3 = 1 -6 = -3 = 13x3 -1 -2
Verify that 1, is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = -11, x1 = (1, 2, –1) 12 = -3, x2 = (-2, 1 0) 13 = -3, x3 = (3, 0, 1) -4 -2 A = -2 -7 6. 1 2 -6 -4 -2 3 1 AX 1 2 = 1,x1 -2 -7 6. 2 11 1 2 -6 -1 -1 -4 -2 -2 -2 Ax2 -2 -7 1 = -3 1 1 2 -6 -4 -2 Ax3 = -2 -7 6. -3 = 13×3 2 -6 1 m O LO
Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. -6 2, = 13, x, = (1, 2, –1) dz = -3, x, = (-2, 1 0) 13 = -3, x, = (3, 0, 1) -1 4 A = 4 5 -12 -2 -4 3 -1 4 -6 1 Ax, = 4 5 -12 = 13 2 = 1,x1 %3D -2 -4 -1 4 -6 Ax2 = 5 -12 4 %3D = -3 -4 -1 4. -6 Ax3 = 4 -12 = 13X3 -3 -2 -4 3
Verify that A, is an eigenvalue of A and that x, is a corresponding eigenvector. -1 4-6 4 5-12 A₁ = 13, x₁ = (1, 2, -1) A₂ = -3, x₂ = (-2,10) -2-4 3] A₂ = -3, x₂ = (3, 0, 1) A = -1 4 -6 4 5-12 -DE- I. -2-4 3 Ax₁ = -1 4 -6 -2 AND Ax₂ = 4 5-12 -2-4 3 -1 = 4 -6 Ax3 = 4 5-12 = 13 = -000- -2-4 3 1 41 2 = ₁x₁ -[] =-3 = 1 = ₂x₂ = 23x3 Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix. (a) the characteristic equation P= (b) the eigenvalues (Enter your answers from smallest to largest.) (d₂d₂)= a basis for each of the corresponding eigenspaces x₁ = For the matrix A, find (if possible) a nonsingular matrix P such that P¹AP is diagonal. (If not possible, enter IMPOSSIBLE.) 2-2 7 03-2 0-1 -888- A = 2 Verify that P-¹AP is a diagonal matrix with the eigenvalues on the main diagonal. p-1AP= 41
Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. 21 = 5, x, = (1, 2, –1) 12 = -3, x, = (-2, 1 0) d3= -3, x, = (3, 0, 1) -2 2 -3 A = 2. 1 -6 -1 -2 -2 2 -3 1 AX 1 2 1 -6 5. = 1,×1 -1 -2 -2 2 -3 Ax2 = 1 -6 = 12X2 2. -1 -2 -2 2 -3 3. -3 Ax3 21 1-6 0. %3D -1 -2
Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. = -11, x¡ = (1, 2, –1) 22 = -3, x, = (-2, 1 0) 23 = -3, x3 = (3, 0, 1) 4 -2 3. A = -2 -7 6 21 %3D %3D 9- %3D -4 -2 3. 1. Ax1 = 2= 1X1 -2 -7 6 = -11 %3D %3D 1 2 -6 -1 -1 -4 -2 3. 2 -2 Ax2 = -2 -7 = -3 %3D %3D 1 2 -6 0. J會 -4 -2 3. 3. Ax3 = -2 -7 -3 %3D %3D %3D 2 -6
Verify that ; is an eigenvalue of A and that x; is a corresponding eigenvector. -4 -2 3 A = -2 -7 6 A₁ = -11, x₁ = (1, 2, -1) 2₂= = -3, x2 = (-2, 10) = -3, x3 = (3, 0, 1) 1 2 -6 13 = -11 = 2₁x₁ 12x2 Ax1 = Ax2 = Ax3 = -4 -2 3 -2 -7 6 1 2 6 -4 -2 3 -2 -7 w 1 2 -1 I -2 = 1 = 0 6 1 2 -6 -4 -2 3 3 -2 -7 6 0 = 1 2 -6 1 00 ↓↑ 000 ↓↑ 000 11 ↓ T 1 2 -1 -2 [1] 0 3 -8 - -3 = 1 = 13x3
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 =
plz help
Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. 3 0 A = [ A₁ = 3, x₁ = (1, 0) 2₂ = -3, x₂ = (0, 1) 0 -3 AX1 ~-[D-F= -0) --- 3 = 0 -3 3 *-*«DE÷-0→ AX2 = = = ไป = 22x2 ↓ 1

SEE MORE QUESTIONS

Recommended textbooks for you

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS