Question

If the null space of a 5 × 8 matrix A is 4-dimensional, what is the dimension of the column space of A? dim Col A-(Simplify your answer.)

Answer 1

Answer: Dim Col A = 4.

Explanation:

Since we have given that

Matrix A has 5 rows and 8 columns.

And Nul A = 4

It implies that the rank of A would be

Number of columns - Nul A = 8 - 4 =4

So, rank A = 4

so, it has dim Col A = 4 also.

But the four vector basis lie in R⁵.

Hence, Dim Col A = 4.