(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given the augmented matrix for a system of equations below, find m such that the system will have infinitely many solutions.

3 3 -9 15

1 -1 3 -3

-4 -4 12 m

m = ?

2. Relevant equations

None

3. The attempt at a solution

Well I tried to reduce the matrix to row-echelon form but I'm not sure what to do with the 'm' at all. I am not familiar with variables in matrices. Here's how far I have gotten:

r1/3 and r3/-4

1 1 -3 5

1 -1 3 -3

1 1 -3 m/-4

r2-r1 and r3-r1

1 1 -3 5

0 1 -3 4

0 0 0 m-5/-4

I don't know how to answer for m. I am pretty sure that infinite solutions means that the matrix needs as many variables as equations which I read somewhere else on the forum.

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# Solve for variable in augmented matrix

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