(i ) 4. (a) Let A = be a 2 x 2 matrix. (i) Compute det(A) and tr(A) (i.e., trace of A which is the sum of the main-diagonal entries). (ii) Is A invertible? Justify your claim. (Hint: Use the result from (i) above!) (iii) Compute the characteristic polynomial of A. (iv) Compute the eigenvalues of A. (v) Compute a basis for each eigenspace of A (i.e., corresponding eigenvector for each eigenvalue obtained in (iv)). (b) Let B = 1 (i }) be a 2 x 2 matrix. Repeat (i)-(v) for B. -2 -3 (c) Let C = be a 2 x 2 matrix. Repeat (i)-(v) for C. 3 -2 2 (d) Let D = -1 be a 2 x 2 matrix. Repeat (i)-(v) for D. (e) Let E = be a 2 x 2 matrix. Repeat (i)-(v) for E. 3 6
(i ) 4. (a) Let A = be a 2 x 2 matrix. (i) Compute det(A) and tr(A) (i.e., trace of A which is the sum of the main-diagonal entries). (ii) Is A invertible? Justify your claim. (Hint: Use the result from (i) above!) (iii) Compute the characteristic polynomial of A. (iv) Compute the eigenvalues of A. (v) Compute a basis for each eigenspace of A (i.e., corresponding eigenvector for each eigenvalue obtained in (iv)). (b) Let B = 1 (i }) be a 2 x 2 matrix. Repeat (i)-(v) for B. -2 -3 (c) Let C = be a 2 x 2 matrix. Repeat (i)-(v) for C. 3 -2 2 (d) Let D = -1 be a 2 x 2 matrix. Repeat (i)-(v) for D. (e) Let E = be a 2 x 2 matrix. Repeat (i)-(v) for E. 3 6
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Please solve B,C,D,E
Transcribed Image Text:4. (a) Let A =
be a 2 x 2 matrix.
(i) Compute det(A) and tr(A) (i.e., trace of A which is the sum of the main-diagonal entries).
(ii) Is A invertible? Justify your claim. (Hint: Use the result from (i) above!)
(iii) Compute the characteristic polynomial of A.
(iv) Compute the eigenvalues of A.
(v) Compute a basis for each eigenspace of A (i.e., corresponding eigenvector for each eigenvalue obtained
in (iv)).
(i )
(b) Let B =
be a 2 x 2 matrix. Repeat (i)-(v) for B.
-2
(c) Let C =
be a 2 x 2 matrix. Repeat (i)-(v) for C.
-2
2 1
(d) Let D =
-1
be a 2 x 2 matrix. Repeat (i)-(v) for D.
4
2,
(e) Let E =
3
be a 2 x 2 matrix. Repeat (i)-(v) for E.
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