Question

Solve the system of equations.

Answer 1

Step 1:

The system of equations are , and .

Convert the equations into matrices form ,

where is coefficient matrix, is constant matrix and is variable matrix.

Dimension of matrix is .

Multiply each side by .

The value of .

Apply identity property of matrix : .

.

Step 2:

First find .

 

Form the matrix .

Use row operations to transform into reduced row echelon form.

Inverse matrix is.

Step 3:

Substitute  in equation (1). 

The solution in ordered pair form is .

Solution:

The solution is .