Question

how do u solve equations in matrixes?

Answer 1

can you give an example?
because there are many problems that use matrixes to solve

Answer 2

There are several ways to solve a system of equation using matrices. For example,
2x + 3y + 4z = 20
x - y + z = 2
3x + z = 6

We can use augmented matrix

2 3 4 | 20
1 -1 1 | 2
3 0 1 | 6

then use row operations to reduce it to reduced row echelon form (RREF), which is

1 0 0 | 1
0 1 0 | 2
0 0 1 | 3

So the answer is {1, 2, 3} or x = 1, y = 2, z = 3

We also can use inverse matrix to solve as follows:
Let A = 2 3 4
1 -1 1
3 9 1
X = x
y
z
B = 20
2
6

Since A X = B, left multiply both sides by A^-1 (the inverse of matrix A)
(A^-1) A X = (A^-1) B
Since (A^-1)A = I, we have
I X = (A^-1) B
Further I X = X, we obtain
X = (A^-1) B

find inverse of a 3x3 matrix is tedious, so we will use calculator to do it, which will get the same result as method #1.