Can somebody suggest how to solve these problems?

1.

U = l(a1, a2, a3)

= (1, 0, 3,−1), = (1,−1, 1, 1), = (1, 1, 5,−3)

W is the solution space of:

+ − = 0

− + = 0.

Find such that:

U = Im( и W = Ker(

2.

L={(,...)|=+}

Find basis which elements are geometrical progression.

3.This the matrix A:

3 -1 1

4 -1 2

2 -1 2

Find such T that the matrix D = is diagonal.Find D.