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-823A16.andA131Do you have enough information to compute the product A-3|? If so, compute it; if not, explain-2clearly why not. AngwerkeyFor 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 leastone column must be a non-pivot column). For part (c), since12-3-1-211and multiplication by A is linear, you do have enough information to compute1-3A-2

(a) It is given that A is 3×4 matrix. The rank of a matrix is the dimension of the row-space. The…

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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 22EQ: Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be...

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