Question

How can I find the N(A), R(A^T), R(A), N(A^T) of the matrix A={(3,4),(6,8)}?

Answer 1

N(A) is the null space of A, R(A) is the range or column space of A. If you see A^T, that is the transpose of A. Meaning the matrix would be A={(3,6),(4,8)}

Answer 2

Lets start with the null space of the matrix. To find the null space of a matrix consider the solution set to Ax = 0

Answer 3

Row reduction will give you the solution set.

Answer 4

The same can be done for the transpose of the matrix. You can find the nullspace by once again finding the solution A^Tx = 0

Answer 5

After row reducing you will see which of the column vectors in the matrix make up the basis for the image.