Question

solve the set of linear equations by the matrices method: a+3b+2c=3, 2a-b-3c=-8,5a+2b+c=9

Answer 1

determinant of coefficient matrix
1 3 2
2 -1 -3
5 2 1
is -28

now replace the first column with the the constants coefficients
3 3 2
-8 -1 -3
9 2 1
and the determinant of that is -56

do a = -56/-28 = 2

now replace the 2nd column with the constants and find the determinant to get b = 84/-28= -3

and similarly replace the 3rd column with the constants to get c = -140/-28 = 5

a = 2
b = -3
c = 5

I used a matrix method called Cramer's Rule
Khan as usual has a nice simple clip explaining how to find the determinant of a 3 by 3 matrix
https://www.khanacademy.org/math/precalculus/precalc-matrices/inverting_matrices/v/finding-the-determinant-of-a-3x3-matrix-method-1

you might also click on his method-2 of the same thing

Answer 2

In google type :

Systems Matrix Calculator

When you see list of result click on :

Online calculator. Linear equations solver: Matrix solution.

When page be open type your coefficients

1 , 3 , 2 , 3

2 , - 1 , - 3 , - 8

5 , 2 , 1 , 9

and click opštion :

Solve the system.

You will see solution step -by step.

Remark :

x1 = a , x2 = b , x3 = c