Linear Algebra Examples

$(x) = (32) (1)$ , $(y) = (43) (- 1)$

Step 1

Remove parentheses.

$x = (32) (1), y = (43) (- 1)$

Step 2

Multiply $32$ by $1$ .

$x = 32, y = (43) (- 1)$

Step 3

Multiply $43$ by $- 1$ .

$x = 32, y = - 43$

Step 4

Write the system of equations in matrix form.

$[\begin{array}{c} 1 & 0 & 32 \\ 0 & 1 & - 43 \end{array}]$

Step 5

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

$x = 32$

$y = - 43$

Step 6

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

$(32, - 43)$

Step 7

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.

$X = [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 32 \\ - 43 \end{array}]$