 Solution

Use Gaussian elimination. Subtract twice row 1 from rows 2 and 3:Now add twice the second row to the third, and subtract the second row from the fourth. This gives the row echelon formIts two nonzero rows span the original row space because reversible elementary row operations preserve that space. They are linearly independent, as witnessed by their leading entries in different columns. ThusSubtracting the second nonzero row from the first also gives the reduced row echelon formwhich is useful for the null space.