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5. Find all values of k for which A is invertible. [k A=0 Lk -k 3 k+1 1 -8 k-1.

5. Find all values of k for which A is invertible. [k A=0 Lk -k 3 k+1 1 -8 k-1.

Advanced Engineering Mathematics
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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5. Find all values of k for which A is invertible. [k 3 A = 0 1 Lk -8 k-1] 6. Assume that A and B are n x n matrices with det A = 3 and det B determinants. -k k+ 1
Transcribed Image Text:5. Find all values of k for which A is invertible. [k 3 A = 0 1 Lk -8 k-1] 6. Assume that A and B are n x n matrices with det A = 3 and det B determinants. -k k+ 1
(a) det(B-¹A) (b) det(3BT) 7. If B is invertible, prove that det(B-¹AB) (c) det(AAT) = det A.
Transcribed Image Text:(a) det(B-¹A) (b) det(3BT) 7. If B is invertible, prove that det(B-¹AB) (c) det(AAT) = det A.
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