# Linear Algebra Examples

,

Subtract from both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .

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

Simplify the left side.

Simplify each term.

Apply the distributive property.

Multiply by .

Cancel the common factor of .

Write as a fraction with denominator .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Multiply and .

Subtract from .

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

Subtract from both sides of the equation.

Simplify the right side of the equation.

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 .

Add and .

Move the negative in front of the fraction.

Divide each term by and simplify.

Divide each term in by .

Simplify the left side of the by cancelling the common factors.

Reduce the expression by cancelling the common factors.

Factor out of .

Move the negative one from the denominator of .

Simplify the expression.

Multiply by .

Rewrite as .

Simplify the right side of the equation.

Multiply by .

Simplify .

Multiply by .

Multiply by .

Multiply and .

Multiply by .

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

Multiply by .

To write as a fraction with a common denominator, 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.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Multiply by .

Multiply by .

Add and .

The solution can be shown in both point and equation forms.

Point Form:

Equation Form: