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.)

Question

Mathematics

Demarcus Schwartz

15 May, 23:41

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.)

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Answers (1)

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Tania Hall · Answer 1

Answer: Dim Col A = 4.

Step-by-step 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.