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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
7 and 5
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8464b8e-d3d1-46f0-bda9-b4682ff11e1d%2Fe77de087-d43b-43af-8711-3675bceb339a%2Fkpaqrx_processed.jpeg&w=3840&q=75)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8464b8e-d3d1-46f0-bda9-b4682ff11e1d%2Fe77de087-d43b-43af-8711-3675bceb339a%2Fog702yn_processed.jpeg&w=3840&q=75)
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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