Linear Algebra Examples

$m = - \frac{1}{5}$ , $b = 1$

Step 1

Write the system of equations in matrix form.

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

Step 2

Find the reduced row echelon form.

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Step 2.1

Swap $R_{2}$ with $R_{1}$ to put a nonzero entry at $1, 1$ .

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

Step 3

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

$b = 1$

$m = - \frac{1}{5}$

Step 4

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

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

Step 5

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.

$X = [\begin{array}{c} b \\ m \end{array}] = [\begin{array}{c} 1 \\ - \frac{1}{5} \end{array}]$