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Suppose A is a 3 x 4 matrix. (a) List all possible values for the rank of A (no justification necessary). (b) List all possible values for the nullity of A (no justification necessary). (c) Suppose you know that 2 3 A 6 and A 2 1 Do you have enough information to compute the product A -3 ? If so, compute it; if not, explain -2 clearly why not.

Suppose A is a 3 x 4 matrix. (a) List all possible values for the rank of A (no justification necessary). (b) List all possible values for the nullity of A (no justification necessary). (c) Suppose you know that 2 3 A 6 and A 2 1 Do you have enough information to compute the product A -3 ? If so, compute it; if not, explain -2 clearly why not.

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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Suppose A is a 3 x 4 matrix. (a) List all possible values for the rank of A (no justification necessary). (b) List all possible values for the nullity of A (no justification necessary). (c) Suppose you know that 個-8 2 3 A 1 6. and A 1 3 1 Do you have enough information to compute the product A -3 |? If so, compute it; if not, explain -2 clearly why not.
Transcribed Image Text:Suppose A is a 3 x 4 matrix. (a) List all possible values for the rank of A (no justification necessary). (b) List all possible values for the nullity of A (no justification necessary). (c) Suppose you know that 個-8 2 3 A 1 6. and A 1 3 1 Do you have enough information to compute the product A -3 |? If so, compute it; if not, explain -2 clearly why not.
Angwer key For part (a), the possible ranks (numbers of pivots) are 0, 1, 2, and 3. For part (b), the possible nullities (numbers of non-pivot columns) are 1, 2, 3, and 4 (since A has four columns but only three rows, at least one column must be a non-pivot column). For part (c), since 1 2 -3 -1 -2 1 1 and multiplication by A is linear, you do have enough information to compute 1 -3 A -2
Transcribed Image Text:Angwer key For part (a), the possible ranks (numbers of pivots) are 0, 1, 2, and 3. For part (b), the possible nullities (numbers of non-pivot columns) are 1, 2, 3, and 4 (since A has four columns but only three rows, at least one column must be a non-pivot column). For part (c), since 1 2 -3 -1 -2 1 1 and multiplication by A is linear, you do have enough information to compute 1 -3 A -2
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