Find the least-squares solution x* of the system

Question

[1 1 1 1, -1 -1 1 1, 1 -1 1 -1] x=[7 -7 5 7]

x*=[ ]

Answer 1

Looks like the matrix given is A transpose which fits the right dimensions.

We need to solve A^TA x^* = A^Tb for x^*

A^TA = [4 0 0]

[0 4 0]

[0 0 4]

A^Tb = [12 12 12]^T

[4 0 0] [12]

[0 4 0] x^* = [12]

[0 0 4] [12]

[3]

x^* = [3]

[3]