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A | B с D Suppose M is the matrix with blocks A, B, C, D. 1. For each of the following 3 cases, write down 1 x 1 matrices A, B, C, D and nullity(A), nullity (M) such that: 1. nullity(M) > nullity(A); 2. nullity (M) = nullity(A); 3. nullity (M) < nullity(A). 2. Prove that in general, rank(M) rank(A).

A | B с D Suppose M is the matrix with blocks A, B, C, D. 1. For each of the following 3 cases, write down 1 x 1 matrices A, B, C, D and nullity(A), nullity (M) such that: 1. nullity(M) > nullity(A); 2. nullity (M) = nullity(A); 3. nullity (M) < nullity(A). 2. Prove that in general, rank(M) rank(A).

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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4. (AB) CD Suppose M is the matrix with blocks A, B, C, D. 1. For each of the following 3 cases, write down 1 x 1 matrices A, B, C, D and nullity (A), nullity (M) such that: 1. nullity (M) > nullity(A); 2. nullity(M) = nullity(A); 3. nullity (M) < nullity(A). 2. Prove that in general, rank(M) ≥ rank(A).
Transcribed Image Text:4. (AB) CD Suppose M is the matrix with blocks A, B, C, D. 1. For each of the following 3 cases, write down 1 x 1 matrices A, B, C, D and nullity (A), nullity (M) such that: 1. nullity (M) > nullity(A); 2. nullity(M) = nullity(A); 3. nullity (M) < nullity(A). 2. Prove that in general, rank(M) ≥ rank(A).
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