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2. If the null space of a 5x6 matrix has dimension = 4, what is the dimension of the row space of A? dim Row A = 2 3. If A is a 4x3 matrix, what is the largest possible dimension of the row space of A? 3 4. If A is a 3x4 matrix, what is the largest possible dimension of the row space of A? 3 5. If A is a 2x5 matrix, explain why it is impossible that dim Nul(A) ? 2. Because Rank A ? 2 thus there are at least 3 free variables thus Nul(A) ? 3

          2. If the null space of a 5x6 matrix has dimension = 4, what is the dimension of the row space of A?
dim Row A = 2
3. If A is a 4x3 matrix, what is the largest possible dimension of the row space of A?
3
4. If A is a 3x4 matrix, what is the largest possible dimension of the row space of A?
3
5. If A is a 2x5 matrix, explain why it is impossible that dim Nul(A) ? 2.
Because Rank A ? 2 thus there are at least
3 free variables thus Nul(A) ? 3

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2. If the null space of a 5x6 matrix has dimension = 4, what is the dimension of the row space of A?
dim Row A = 2
3. If A is a 4x3 matrix, what is the largest possible dimension of the row space of A?
3
4. If A is a 3x4 matrix, what is the largest possible dimension of the row space of A?
3
5. If A is a 2x5 matrix, explain why it is impossible that dim Nul(A) ? 2.
Because Rank A ? 2 thus there are at least
3 free variables thus Nul(A) ? 3

Added by Seth A.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Adi S

04/18/2023

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Step 1: Given that A is a 4x3 matrix, the row space of A has dimension 4. Show more…

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2. If the null space of a 5x6 matrix has dimension = 4, what is the dimension of the row space of A? 3. If A is a 4x3 matrix, what is the largest possible dimension of the row space of A? 4. If A is a 3x4 matrix, what is the largest possible dimension of the row space of A? 5. If A is a 2x5 matrix, explain why it is impossible that dim Nul(A) ≤ 2.

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