# Linear Algebra Examples

The matrix equation can be written as a set of equations.

Solve for in the first equation.

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Solve for in the second equation.

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Solve for in the third equation.

Simplify .

Simplify the numerator.

Simplify .

Write as a fraction with denominator .

Multiply and .

Multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Multiply and .

Simplify .

Simplify each term.

Simplify the numerator.

Write as a fraction with denominator .

Multiply and .

Multiply by .

Multiply the numerator by the reciprocal of the denominator.

Simplify .

Multiply and .

Multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.