# Linear Algebra Examples

Step 1

Write as an augmented matrix for .

Step 2

Step 2.1

Multiply each element of by to make the entry at a .

Step 2.1.1

Multiply each element of by to make the entry at a .

Step 2.1.2

Simplify .

Step 2.2

Perform the row operation to make the entry at a .

Step 2.2.1

Perform the row operation to make the entry at a .

Step 2.2.2

Simplify .

Step 2.3

Perform the row operation to make the entry at a .

Step 2.3.1

Perform the row operation to make the entry at a .

Step 2.3.2

Simplify .

Step 2.4

Perform the row operation to make the entry at a .

Step 2.4.1

Perform the row operation to make the entry at a .

Step 2.4.2

Simplify .

Step 2.5

Perform the row operation to make the entry at a .

Step 2.5.1

Perform the row operation to make the entry at a .

Step 2.5.2

Simplify .

Step 2.6

Multiply each element of by to make the entry at a .

Step 2.6.1

Multiply each element of by to make the entry at a .

Step 2.6.2

Simplify .

Step 2.7

Perform the row operation to make the entry at a .

Step 2.7.1

Perform the row operation to make the entry at a .

Step 2.7.2

Simplify .

Step 2.8

Perform the row operation to make the entry at a .

Step 2.8.1

Perform the row operation to make the entry at a .

Step 2.8.2

Simplify .

Step 2.9

Perform the row operation to make the entry at a .

Step 2.9.1

Perform the row operation to make the entry at a .

Step 2.9.2

Simplify .

Step 2.10

Perform the row operation to make the entry at a .

Step 2.10.1

Perform the row operation to make the entry at a .

Step 2.10.2

Simplify .

Step 2.11

Multiply each element of by to make the entry at a .

Step 2.11.1

Multiply each element of by to make the entry at a .

Step 2.11.2

Simplify .

Step 2.12

Perform the row operation to make the entry at a .

Step 2.12.1

Perform the row operation to make the entry at a .

Step 2.12.2

Simplify .

Step 2.13

Perform the row operation to make the entry at a .

Step 2.13.1

Perform the row operation to make the entry at a .

Step 2.13.2

Simplify .

Step 2.14

Perform the row operation to make the entry at a .

Step 2.14.1

Perform the row operation to make the entry at a .

Step 2.14.2

Simplify .

Step 2.15

Multiply each element of by to make the entry at a .

Step 2.15.1

Multiply each element of by to make the entry at a .

Step 2.15.2

Simplify .

Step 2.16

Perform the row operation to make the entry at a .

Step 2.16.1

Perform the row operation to make the entry at a .

Step 2.16.2

Simplify .

Step 2.17

Perform the row operation to make the entry at a .

Step 2.17.1

Perform the row operation to make the entry at a .

Step 2.17.2

Simplify .

Step 2.18

Perform the row operation to make the entry at a .

Step 2.18.1

Perform the row operation to make the entry at a .

Step 2.18.2

Simplify .

Step 2.19

Perform the row operation to make the entry at a .

Step 2.19.1

Perform the row operation to make the entry at a .

Step 2.19.2

Simplify .

Step 2.20

Perform the row operation to make the entry at a .

Step 2.20.1

Perform the row operation to make the entry at a .

Step 2.20.2

Simplify .

Step 2.21

Perform the row operation to make the entry at a .

Step 2.21.1

Perform the row operation to make the entry at a .

Step 2.21.2

Simplify .

Step 2.22

Perform the row operation to make the entry at a .

Step 2.22.1

Perform the row operation to make the entry at a .

Step 2.22.2

Simplify .

Step 2.23

Perform the row operation to make the entry at a .

Step 2.23.1

Perform the row operation to make the entry at a .

Step 2.23.2

Simplify .

Step 3

Use the result matrix to declare the final solution to the system of equations.

Step 4

Write a solution vector by solving in terms of the free variables in each row.

Step 5

Write as a solution set.