# Linear Algebra Examples

,

Step 1

Find the from the system of equations.

Step 2

The inverse of a matrix can be found using the formula where is the determinant of .

If then

Find the determinant of .

These are both valid notations for the determinant of a matrix.

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Subtract from .

Substitute the known values into the formula for the inverse of a matrix.

Simplify each element in the matrix.

Rearrange .

Rearrange .

Multiply by each element of the matrix.

Simplify each element in the matrix.

Rearrange .

Rearrange .

Rearrange .

Rearrange .

Step 3

Left multiply both sides of the matrix equation by the inverse matrix.

Step 4

Any matrix multiplied by its inverse is equal to all the time. .

Step 5

Multiply each row in the first matrix by each column in the second matrix.

Simplify each element of the matrix by multiplying out all the expressions.

Step 6

Simplify the left and right side.

Step 7

Find the solution.