Technology matrix

Let S={X1,X2,X3} be a linearly independent set of vectors in R^3. How to determine whether T={2X1 + X2 - 2X3,4X1+ 3X2,3X1 + 2X2 - X3} is linearly independent. Justify your answer please.

If X1,X2 and X3 are vectors in R3 such that {X1,X2} and {X1,X3} are linearly independent sets, then {X1,X2,X3} is a linearly independent set.

               2 1 0                   1 0 1Let A = [ 1 0 1 ] and B = [ 2 0 1 ]                0 3 0                  0 1 1 Find the matrix X such that (2X + A)-1 = B.

If A is a 2 x 2 matrix such that AAT (Transpose) = 0, then A = 0.