Linear Algebra Examples

$a = - x + 5.5$ , $b = 0.33 x + 1.5$

Step 1

Add $x$ to both sides of the equation.

$a + x = 5.5, b = 0.33 x + 1.5$

Step 2

Subtract $0.33 x$ from both sides of the equation.

$a + x = 5.5, b - 0.33 x = 1.5$

Step 3

Write the system of equations in matrix form.

$[\begin{array}{c} 1 & 0 & 1 & 5.5 \\ 0 & 1 & - 0.33 & 1.5 \end{array}]$

Step 4

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

$a + x = 5.5$

$b - 0.33 x = 1.5$

Step 5

Subtract $x$ from both sides of the equation.

$a = 5.5 - x$

$b - 0.33 x = 1.5$

Step 6

Add $0.33 x$ to both sides of the equation.

$b = 1.5 + 0.33 x$

$a = 5.5 - x$

Step 7

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

$(5.5 - x, 1.5 + 0.33 x, x)$

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.

$X = [\begin{array}{c} a \\ b \\ x \end{array}] = [\begin{array}{c} 5.5 - x \\ 1.5 + 0.33 x \\ x \end{array}]$