4.[ A B Suppose M is the matrix with blocks A, B, C, D. CD 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).

FINANCIAL ACCOUNTING
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Chapter1: Financial Statements And Business Decisions
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4.[
A B
Suppose M is the matrix
with blocks A, B, C, D.
CD
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.[ A B Suppose M is the matrix with blocks A, B, C, D. CD 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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