# Square Matrix with Determinant Equal to 0 and Basis for a Solution Space

1) Let A be a square matrix with determinant equal to 0. Prove that if X is a solution to the equation Ax=b then every solution to this equation must have the form x=X+xot where xo is a solution of Ax=0.

2) Find a basis for the solution space of the following system of equations.

x- 2x2+ x3 =-4

-2x +3x2 + x4=6

3x -3x2 -3x3 -12x4=-6

-3x +5x2 -x3 +4x4=10

https://brainmass.com/math/matrices/square-matrix-determinant-equal-basis-solution-space-154738

#### Solution Preview

1) Let A be a square matrix with determinant equal to 0. Prove that if X is a solution to the equation Ax = b then every solution to this equation must have the form x = X + xo where xo is a solution of Ax = 0.

Since x0 is a solution to Ax = 0, we have Ax0 = 0 ......(i)

Since X is ...

#### Solution Summary

A square matrix with determinant equal to 0 and a basis for a solution space are investigated. The solution is detailed and well presented.