6. Prove that I M is an n x n matrix that has a DIOCK Iorm A B (18) where the sizes of A, B, C are k x k, k× (n − k) and (n − k) × (n − k) respectively, then det (M) = det (A) det(C). M =
6. Prove that I M is an n x n matrix that has a DIOCK Iorm A B (18) where the sizes of A, B, C are k x k, k× (n − k) and (n − k) × (n − k) respectively, then det (M) = det (A) det(C). M =
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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![**6. Prove that if \( M \) is an \( n \times n \) matrix that has a "block form"**
\[ M = \begin{pmatrix} A & B \\ 0 & C \end{pmatrix} \]
**where the sizes of \( A, B, C \) are \( k \times k \), \( k \times (n-k) \), and \( (n-k) \times (n-k) \) respectively, then**
\[ \det(M) = \det(A) \det(C). \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32f77ee0-291c-46d0-b315-80fb2fd096d8%2F89ef3520-f5ff-4fbe-99f4-8a764444a781%2F6n2obch_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**6. Prove that if \( M \) is an \( n \times n \) matrix that has a "block form"**
\[ M = \begin{pmatrix} A & B \\ 0 & C \end{pmatrix} \]
**where the sizes of \( A, B, C \) are \( k \times k \), \( k \times (n-k) \), and \( (n-k) \times (n-k) \) respectively, then**
\[ \det(M) = \det(A) \det(C). \]
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