Define a real linear transformationL1 : R4 \to R2 by

L1(x1, x2, x3, x4) = (3x1 + x2 + 2x3 − x4, 2x1 + 4x2 + 5x3 − x4)

and let U1 denote the kernel of L1. Define a real linear transformation L2 : R4 ! R2 by

L2(x1, x2, x3, x4) = (5x1 + 7x2 + 11x3 + 3x4, 2x1 + 6x2 + 9x3 + 4x4)

and let U2 denote the kernel of L2.

Construct bases for U1, U2, U1 &U2 and U1 + U2.

Not sure on how to tackle this question. Or how to construct basis in similar questions. Any help would be appreciated a lot!