Let A be a kxk matrix and let B be an (n-k) × (n - k) matrix. Let E = F = Ik ·[8]. O B A c- [68] C = B A 0 In-k TO) where Ik Ik and In-k are the (n-k) × (n - k) identity matrices. (a) Show that det(E) = det(B). (b) Show that det(F) = det(A). (c) Show that det(C) = det(A) det(B). Let A and B be k x k matrices and let M = k x k B = [28] A Show that det(M) ( 1) det(A) det(R) and
Let A be a kxk matrix and let B be an (n-k) × (n - k) matrix. Let E = F = Ik ·[8]. O B A c- [68] C = B A 0 In-k TO) where Ik Ik and In-k are the (n-k) × (n - k) identity matrices. (a) Show that det(E) = det(B). (b) Show that det(F) = det(A). (c) Show that det(C) = det(A) det(B). Let A and B be k x k matrices and let M = k x k B = [28] A Show that det(M) ( 1) det(A) det(R) and
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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Plz fo both questions
![18. Let
A be a kxk matrix and let B be an
(n − k) × (n − k) matrix. Let
Ik
E
² = (1 8).
B
C =
F =
A
= [68]
B
=
M =
A
O In-k
2).
where Ik and
In-k
(n − k) × (n − k) identity matrices.
(a) Show that det(E) = det(B).
(b) Show that det(F) = det(A).
(c) Show that det(C) = det(A) det(B).
19. Let A and B be k x k matrices and let
are the k x k
[ B]
A
Show that det(M) = (−1)k det(A) det(B).
and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F572394d6-763b-4634-a070-d7c873f29a55%2F1fb9a85d-f445-4171-9fe1-939b6c09256a%2Fz09tlu_processed.png&w=3840&q=75)
Transcribed Image Text:18. Let
A be a kxk matrix and let B be an
(n − k) × (n − k) matrix. Let
Ik
E
² = (1 8).
B
C =
F =
A
= [68]
B
=
M =
A
O In-k
2).
where Ik and
In-k
(n − k) × (n − k) identity matrices.
(a) Show that det(E) = det(B).
(b) Show that det(F) = det(A).
(c) Show that det(C) = det(A) det(B).
19. Let A and B be k x k matrices and let
are the k x k
[ B]
A
Show that det(M) = (−1)k det(A) det(B).
and
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