# How do you solve the system #3a+2b=27, 6a-7b+c=5, -2a+10b+5c=-29# using matrices?

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The solution is

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We perform the Gauss Jordan elimination with the augmented matrix

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3a + 2b = 27

6a - 7b + c = 5

-2a + 10b +5c = -29

First, convert the left side of the equations into a matrix called 'A'. Inside the matrix, put in the coeffecients of each of the variables in the equations above.

A=

Now, do the same for right side of the equation and convert the numbers into a matrix called 'b'.

b=

Use the formula

Rearrange for

If you need to do it by hand, here are some videos from Khan Academy on how to do it. I did mine using Symbolab.

Therefore,

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