Is Matrix A Invertible? Solving Linear System with Gaussian Elimination

[gpax42]

Homework Statement

Suppose that Gaussian Elimination gives the soluiton of a Linear System Ax=c as x = x₀ + a₁x₁ + a₂x₂, where A is a 6X6 matrix and a₁ and a₂ are arbitrary. Is the matrix A invertible? Explain

The Attempt at a Solution

I simply explained that due to properties of an invertible matrix, Ax=c must have exactly one solution but if a₁ and ₂ are arbitrary, then x = x₀ + a₁x₁ + a₂x₂ has infinitely many solutions and A cannot be invertible

does anyone agree with this answer and if not, any advice on how to start the problem would be great appreciated thanks a lot!

 

[Mark44]

I'm assuming that x₀, x₁, and x₂ are vectors. Your reasoning looks fine to me. If A had been invertible then you would have gotten a unique solution, which could be written as x = A^-1c.