- #1

- 118

- 5

## Homework Statement

Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values.

x

_{1}−2x

_{2}+2x

_{3}= −1

−3x

_{1}+ax

_{2}−10x

_{3}= 5

x

_{1}+x

_{2}−4x

_{3}= 3

## Homework Equations

Augmented Matrix

## The Attempt at a Solution

1 -2 2 -1

-3 a -10 5

1 1 -4 3

I switched the row with the variable to the bottom.

1 -2 2 -1

1 1 -4 3

-3 a -10 5

I minused Row 1 from Row 2

1 -2 2 -1

0 3 -6 5

-3 a -10 5

3Row 1 + Row 3

1 -2 2 -1

0 3 -6 5

0 (a-6) -4 2

Here is where I get confused. I don't know how to get the 3 in row 2 to equal 1 and get the (a-6) to equal 0.

Any advice as to where I went wrong or what I need to do next would be greatly appreciated!