# Linear Algebra Examples

,

Step 1

Represent the system of equations in matrix format.

Step 2

Step 2.1

Write in determinant notation.

Step 2.2

The determinant of a matrix can be found using the formula .

Step 2.3

Simplify the determinant.

Step 2.3.1

Simplify each term.

Step 2.3.1.1

Multiply by .

Step 2.3.1.2

Multiply by .

Step 2.3.2

Add and .

Step 3

Since the determinant is not , the system can be solved using Cramer's Rule.

Step 4

Step 4.1

Replace column of the coefficient matrix that corresponds to the -coefficients of the system with .

Step 4.2

Find the determinant.

Step 4.2.1

The determinant of a matrix can be found using the formula .

Step 4.2.2

Simplify the determinant.

Step 4.2.2.1

Simplify each term.

Step 4.2.2.1.1

Multiply by .

Step 4.2.2.1.2

Multiply by .

Step 4.2.2.2

Add and .

Step 4.3

Use the formula to solve for .

Step 4.4

Substitute for and for in the formula.

Step 4.5

Divide by .

Step 5

Step 5.1

Replace column of the coefficient matrix that corresponds to the -coefficients of the system with .

Step 5.2

Find the determinant.

Step 5.2.1

The determinant of a matrix can be found using the formula .

Step 5.2.2

Simplify the determinant.

Step 5.2.2.1

Simplify each term.

Step 5.2.2.1.1

Multiply by .

Step 5.2.2.1.2

Multiply by .

Step 5.2.2.2

Add and .

Step 5.3

Use the formula to solve for .

Step 5.4

Substitute for and for in the formula.

Step 5.5

Divide by .

Step 6

List the solution to the system of equations.