How to Make the System Consistent: Solving for Alpha in an Augmented Matrix

[Cpt Qwark]

Homework Statement

\begin{array}{rrr|r} -1 & 2 & -1 & -3 \\ 2 & 3 & α-1 & α-4 \\ 3 & 1 & α & 1 \end{array}

$$α∈ℝ$$
for the augmented matrix, what value of α would make the system consistent?

Homework Equations

N/A
Answer: α=2

The Attempt at a Solution

I know that the system has to have an infinite or unique amount of solutions to be consistent and you have to perform Gaussian elimination?

 

[Ray Vickson]

Homework Statement

\begin{array}{rrr|r} -1 & 2 & -1 & -3 \\ 2 & 3 & α-1 & α-4 \\ 3 & 1 & α & 1 \end{array}

$$α∈ℝ$$
for the augmented matrix, what value of α would make the system consistent?

Homework Equations

N/A
Answer: α=2

The Attempt at a Solution

I know that the system has to have an infinite or unique amount of solutions to be consistent and you have to perform Gaussian elimination?

If you think that Gaussian elimination is (maybe) the way to go, then just do it! That way you will find out if it works, or not. That is the very best way to learn.