# Precalculus Examples

Step 1

Step 1.1

Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is and the second matrix is .

Step 1.2

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

Step 2

Write as a linear system of equations.

Step 3

Step 3.1

Solve for in .

Step 3.1.1

Subtract from both sides of the equation.

Step 3.1.2

Divide each term in by and simplify.

Step 3.1.2.1

Divide each term in by .

Step 3.1.2.2

Simplify the left side.

Step 3.1.2.2.1

Cancel the common factor of .

Step 3.1.2.2.1.1

Cancel the common factor.

Step 3.1.2.2.1.2

Divide by .

Step 3.1.2.3

Simplify the right side.

Step 3.1.2.3.1

Move the negative in front of the fraction.

Step 3.2

Replace all occurrences of with in each equation.

Step 3.2.1

Replace all occurrences of in with .

Step 3.2.2

Simplify the left side.

Step 3.2.2.1

Simplify .

Step 3.2.2.1.1

Simplify each term.

Step 3.2.2.1.1.1

Apply the distributive property.

Step 3.2.2.1.1.2

Cancel the common factor of .

Step 3.2.2.1.1.2.1

Factor out of .

Step 3.2.2.1.1.2.2

Cancel the common factor.

Step 3.2.2.1.1.2.3

Rewrite the expression.

Step 3.2.2.1.1.3

Cancel the common factor of .

Step 3.2.2.1.1.3.1

Move the leading negative in into the numerator.

Step 3.2.2.1.1.3.2

Factor out of .

Step 3.2.2.1.1.3.3

Cancel the common factor.

Step 3.2.2.1.1.3.4

Rewrite the expression.

Step 3.2.2.1.1.4

Multiply by .

Step 3.2.2.1.2

Add and .

Step 3.3

Move all terms not containing to the right side of the equation.

Step 3.3.1

Subtract from both sides of the equation.

Step 3.3.2

Subtract from .

Step 3.4

Replace all occurrences of with in each equation.

Step 3.4.1

Replace all occurrences of in with .

Step 3.4.2

Simplify the right side.

Step 3.4.2.1

Simplify .

Step 3.4.2.1.1

Combine the numerators over the common denominator.

Step 3.4.2.1.2

Simplify the expression.

Step 3.4.2.1.2.1

Multiply by .

Step 3.4.2.1.2.2

Add and .

Step 3.4.2.1.2.3

Divide by .

Step 3.5

List all of the solutions.