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.