Linear Algebra Examples

$x + 2 = 1$ , $y - 2 = 5$

Step 1

Subtract $2$ from both sides of the equation.

$x = 1 - 2, y - 2 = 5$

Step 2

Subtract $2$ from $1$ .

$x = - 1, y - 2 = 5$

Step 3

Add $2$ to both sides of the equation.

$x = - 1, y = 5 + 2$

Step 4

Add $5$ and $2$ .

$x = - 1, y = 7$

Step 5

Write the system of equations in matrix form.

$[\begin{array}{c} 1 & 0 & - 1 \\ 0 & 1 & 7 \end{array}]$

Step 6

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

$x = - 1$

$y = 7$

Step 7

The solution is the set of ordered pairs that makes the system true.

$(- 1, 7)$

Step 8

Decompose a solution vector by re-arranging each equation represented in the row-reduced form of the augmented matrix by solving for the dependent variable in each row yields the vector equality.

$X = [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} - 1 \\ 7 \end{array}]$