# 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 .
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.
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 .
Simplify.
Simplify the right side.
Simplify the numerator.
Simplify .
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 the numerators over the common denominator.
Simplify the numerator.
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 the right side.
Simplify each term.
Simplify the numerator.
Write as a fraction with denominator .
Multiply and .
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
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 .
Multiply by .