Given the matrix A 1 2 0 3 6 0 2 5 5 0 2 10 0 3 15 Find a n

Given the matrix A = [1 2 0 3 6 0 -2 -5 5 0 -2 10 0 -3 15], Find a nonzero vector In the column space of A. Find a nonzero vector in the null space of A. Is [1, -1, 1] in the column space of A?

Solution

We will reduce A to its RREF as under:

Then the RREF of A is