Let A, B, C, and D be n x n matrices with A invertible. a. Find matrices X and Y to produce the block LU factorization [a })=[{ ЯТЕ B B D and then show that det Ĉ BI= (det A) · det(D – CA-' B) b. Show that if AC = CA, then [¿ 5] det = det(AD – CB) – CB) D
Let A, B, C, and D be n x n matrices with A invertible. a. Find matrices X and Y to produce the block LU factorization [a })=[{ ЯТЕ B B D and then show that det Ĉ BI= (det A) · det(D – CA-' B) b. Show that if AC = CA, then [¿ 5] det = det(AD – CB) – CB) D
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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![Let A, B, C, and D be n x n matrices with A invertible.
a. Find matrices X and Y to produce the block LU factorization
[a
})=[{
ЯТЕ
B
B
D
and then show that
det Ĉ BI= (det A) · det(D – CA-' B)
b. Show that if AC = CA, then
[¿ 5]
det
= det(AD – CB)
– CB)
D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6d3bc04-9959-4958-bc17-db1a8819e3b8%2Fb8d43401-08d6-4be9-8293-aa8c0e02a73a%2F33o591g.png&w=3840&q=75)
Transcribed Image Text:Let A, B, C, and D be n x n matrices with A invertible.
a. Find matrices X and Y to produce the block LU factorization
[a
})=[{
ЯТЕ
B
B
D
and then show that
det Ĉ BI= (det A) · det(D – CA-' B)
b. Show that if AC = CA, then
[¿ 5]
det
= det(AD – CB)
– CB)
D
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