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Answer : Dimension of column A is also be 4 whereas the two vector basis lie in R⁴.

The smallest possible dimension of Nul A would be zero.

Step-by-step explanation:

Since we have given that

A is matrix of 4 x 9 .

so, Number of rows = 4

Number of columns = 9

Nul A = 5

It means that Rank of A would be 9 - 5 =4

So, rank A = 4

Thus, dimension of column A is also be 4 whereas the four vector basis lie in R⁴.

So, dim Col A = 4

If A is 7 x  3 matrix.

So, we know that

rank A + dim (null A) = 3

so, it is possible to have rank A = 3 so the dim col A should be 3

Then the smallest possible dimension of Nul A would be zero.