Linear Algebra Examples

$a = \frac{5}{2}$ , $d = - \frac{1}{2}$

Step 1

Write the system of equations in matrix form.

$[\begin{array}{c} 1 & 0 & \frac{5}{2} \\ 0 & 1 & - \frac{1}{2} \end{array}]$

Step 2

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

$a = \frac{5}{2}$

$d = - \frac{1}{2}$

Step 3

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

$(\frac{5}{2}, - \frac{1}{2})$

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.

$X = [\begin{array}{c} a \\ d \end{array}] = [\begin{array}{c} \frac{5}{2} \\ - \frac{1}{2} \end{array}]$