3-2 1 Let A = -2 -2 6-2 -2 3 1 (1)The eigenvalues of A are A1,2 = -2 and A3 = -8. T Which of the following statements are true? (ii) P₁ = [-2-10] and P₂ = [-2 0 2] are eigenvectors corre- sponding to A1,2 = 2. (iii) P3 = [1/2-1 1/2] is an eigenvector corresponding to A3 = -8. (iv) Q₁ = [2 1 0], Q2 = [-1/5 2/5 1], and Q3 = [1 -2 17 eigenvectors of A. are (v) The matrix Q whose columns are 1/591. 5 √5 √30 V63 diagonalizes A, where Q1, Q2, and Q3 are given in statement (iv). (vi) The matrix Q in statement (v) satisfies QTeAt Q = diag(e-2t, e-2t, e-st). A) () (), and (vi) OB) () () (), and (v) OC) ), (iv). (v) and (vi) OD) (). (iv), and (v) O E) () (). (v). (v) and (vi)
3-2 1 Let A = -2 -2 6-2 -2 3 1 (1)The eigenvalues of A are A1,2 = -2 and A3 = -8. T Which of the following statements are true? (ii) P₁ = [-2-10] and P₂ = [-2 0 2] are eigenvectors corre- sponding to A1,2 = 2. (iii) P3 = [1/2-1 1/2] is an eigenvector corresponding to A3 = -8. (iv) Q₁ = [2 1 0], Q2 = [-1/5 2/5 1], and Q3 = [1 -2 17 eigenvectors of A. are (v) The matrix Q whose columns are 1/591. 5 √5 √30 V63 diagonalizes A, where Q1, Q2, and Q3 are given in statement (iv). (vi) The matrix Q in statement (v) satisfies QTeAt Q = diag(e-2t, e-2t, e-st). A) () (), and (vi) OB) () () (), and (v) OC) ), (iv). (v) and (vi) OD) (). (iv), and (v) O E) () (). (v). (v) and (vi)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![3
-2
1
-2
6 -2
1
-2 3
(i) The eigenvalues of A are A1,2 = -2 and A3 = -8.
(ii) P₁ = [-2 -1 0] and P₂ = [-2 0 2] are eigenvectors corre-
sponding to A1,2 = 2.
(iii) P3= [1/2 -1 1/2] is an eigenvector corresponding to X3 = -8.
(iv) Q₁ = [2 1 0], Q₂ = [-1/5 2/5 1], and Q3 = [1 -2 1] a
are
eigenvectors of A.
Let A =
1
5
(v) The matrix Q whose columns are Q₁₁ Q₂, Q3 diagonalizes
√30
A, where Q1, Q2, and Q3 are given in statement (iv).
(vi) The matrix Q in statement (v) satisfies QTeAt Q = diag(e-2t, e-2t e-st).
√6
OA) () (), and (vi)
Which of the following statements are true?
B) (i), (i), (v), and (v)
OC) (i), (iv). (v) and (vi)
OD) (). (iv), and (v)
O E) () (). (v). (v) and (vi)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc91ca9bc-f1a4-4ccd-9d92-ad4a596a80e8%2F807db881-4b93-420f-8124-c6eab45100c8%2Fx5vxwze_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3
-2
1
-2
6 -2
1
-2 3
(i) The eigenvalues of A are A1,2 = -2 and A3 = -8.
(ii) P₁ = [-2 -1 0] and P₂ = [-2 0 2] are eigenvectors corre-
sponding to A1,2 = 2.
(iii) P3= [1/2 -1 1/2] is an eigenvector corresponding to X3 = -8.
(iv) Q₁ = [2 1 0], Q₂ = [-1/5 2/5 1], and Q3 = [1 -2 1] a
are
eigenvectors of A.
Let A =
1
5
(v) The matrix Q whose columns are Q₁₁ Q₂, Q3 diagonalizes
√30
A, where Q1, Q2, and Q3 are given in statement (iv).
(vi) The matrix Q in statement (v) satisfies QTeAt Q = diag(e-2t, e-2t e-st).
√6
OA) () (), and (vi)
Which of the following statements are true?
B) (i), (i), (v), and (v)
OC) (i), (iv). (v) and (vi)
OD) (). (iv), and (v)
O E) () (). (v). (v) and (vi)
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VIEWStep 2: We find Eigen vectors corresponding to the eigen values of matrix A .
VIEWStep 3: We give definition of eigen vector.
VIEWStep 4: We give definition of diagonalization of a matrix.
VIEWStep 5: We check option vi .
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