Let A be a 3x5 matrix (a) Give all possible values for the rank of A (b) If the rank of A is 3, what is the dimension of its columnspace (c) If the rank of A is 3, what is the dimension of the solutionspace of the homogeneous system Ax=0

OlmekinjP

OlmekinjP

Answered question

2021-01-08

A should be a 3x5 matrix
(a) Give every potential rank of A value 
(b) What is the size of A's columnspace if its rank is 3?

(c) What is the dimension of the solutionspace for the homogeneous system Ax=0 if the rank of A is 3?

Answer & Explanation

SabadisO

SabadisO

Skilled2021-01-09Added 108 answers

( A) : All possible values for the rank of matrix A is i.e. 0 ,1,2,3
(b) : if the rank of a matrix is 3 then the dimension of itscolumn space = rank of A = 3.
(c) : rank A =3 so the dimension of solution space = dim of null spaceof A = 5 - 3 =2.

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