Linear Algebra Examples

$u = 5$ , $w = 5$ , $x = 45$

Step 1

Write the system of equations in matrix form.

$[\begin{array}{c} 1 & 0 & 0 & 5 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 1 & 45 \end{array}]$

Step 2

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

$u = 5$

$w = 5$

$x = 45$

Step 3

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

$(5, 5, 45)$

Step 4

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.

$X = [\begin{array}{c} u \\ w \\ x \end{array}] = [\begin{array}{c} 5 \\ 5 \\ 45 \end{array}]$