Solve the Matrix Equation 3x-2[[1.5,-2.4],[3.6,-0.5]]=[[1.2,-3.6],[0.3,0.4]]

$3 x - 2 [\begin{array}{c} 1.5 & - 2.4 \\ 3.6 & - 0.5 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}]$

Multiply $- 2$ by each element of the matrix.

$3 x + [\begin{array}{c} - 2 \cdot 1.5 & - 2 \cdot - 2.4 \\ - 2 \cdot 3.6 & - 2 \cdot - 0.5 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}]$

Simplify each element in the matrix.

Rearrange $- 2 \cdot 1.5$ .

$3 x + [\begin{array}{c} - 3 & - 2 \cdot - 2.4 \\ - 2 \cdot 3.6 & - 2 \cdot - 0.5 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}]$

Rearrange $- 2 \cdot - 2.4$ .

$3 x + [\begin{array}{c} - 3 & 4.8 \\ - 2 \cdot 3.6 & - 2 \cdot - 0.5 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}]$

Rearrange $- 2 \cdot 3.6$ .

$3 x + [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & - 2 \cdot - 0.5 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}]$

Rearrange $- 2 \cdot - 0.5$ .

$3 x + [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & 1 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}]$

Subtract the matrix from both sides of the equation.

$3 X + [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & 1 \end{array}] - [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & 1 \end{array}] = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}] - [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & 1 \end{array}]$

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} - 3 - (- 3) & 4.8 - 4.8 \\ - 7.2 - (- 7.2) & 1 - 1 \end{array}] + 3 X = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}] - [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & 1 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 3 - (- 3) & 4.8 - 4.8 \\ - 7.2 - (- 7.2) & 1 - 1 \end{array}]$ .

Simplify $- 3 - (- 3)$ .

$[\begin{array}{c} 0 & 4.8 - 4.8 \\ - 7.2 - (- 7.2) & 1 - 1 \end{array}] + 3 X = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}] - [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & 1 \end{array}]$

Simplify $4.8 - 4.8$ .

$[\begin{array}{c} 0 & 0 \\ - 7.2 - (- 7.2) & 1 - 1 \end{array}] + 3 X = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}] - [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & 1 \end{array}]$

Simplify $- 7.2 - (- 7.2)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 1 - 1 \end{array}] + 3 X = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}] - [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & 1 \end{array}]$

Simplify $1 - 1$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 1.2 & - 3.6 \\ 0.3 & 0.4 \end{array}] - [\begin{array}{c} - 3 & 4.8 \\ - 7.2 & 1 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 1.2 - (- 3) & - 3.6 - 4.8 \\ 0.3 - (- 7.2) & 0.4 - 1 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 1.2 - (- 3) & - 3.6 - 4.8 \\ 0.3 - (- 7.2) & 0.4 - 1 \end{array}]$ .

Simplify $1.2 - (- 3)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 4.2 & - 3.6 - 4.8 \\ 0.3 - (- 7.2) & 0.4 - 1 \end{array}]$

Simplify $- 3.6 - 4.8$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 4.2 & - 8.4 \\ 0.3 - (- 7.2) & 0.4 - 1 \end{array}]$

Simplify $0.3 - (- 7.2)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & 0.4 - 1 \end{array}]$

Simplify $0.4 - 1$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + 3 X = [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & - 0.6 \end{array}]$

Adding the null matrix to any matrix is a matrix itself.

$3 X = [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & - 0.6 \end{array}]$

Multiply both sides of the equation by $\frac{1}{3}$ .

$\frac{1}{3} \cdot (3 X) = \frac{1}{3} \cdot [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & - 0.6 \end{array}]$

Simplify both sides of the equation.

Cancel the common factor of $3$ .

Factor $3$ out of $3 X$ .

$\frac{1}{3} \cdot (3 (X)) = \frac{1}{3} \cdot [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & - 0.6 \end{array}]$

Cancel the common factor.

$\frac{1}{3} \cdot (3 X) = \frac{1}{3} \cdot [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & - 0.6 \end{array}]$

Rewrite the expression.

$X = \frac{1}{3} \cdot [\begin{array}{c} 4.2 & - 8.4 \\ 7.5 & - 0.6 \end{array}]$

Simplify the right side of the equation.

Multiply $\frac{1}{3}$ by each element of the matrix.

$X = [\begin{array}{c} \frac{1}{3} \cdot 4.2 & \frac{1}{3} \cdot - 8.4 \\ \frac{1}{3} \cdot 7.5 & \frac{1}{3} \cdot - 0.6 \end{array}]$

Simplify each element in the matrix.

Rearrange $\frac{1}{3} \cdot 4.2$ .

$X = [\begin{array}{c} 1.4 & \frac{1}{3} \cdot - 8.4 \\ \frac{1}{3} \cdot 7.5 & \frac{1}{3} \cdot - 0.6 \end{array}]$

Rearrange $\frac{1}{3} \cdot - 8.4$ .

$X = [\begin{array}{c} 1.4 & - 2.8 \\ \frac{1}{3} \cdot 7.5 & \frac{1}{3} \cdot - 0.6 \end{array}]$

Rearrange $\frac{1}{3} \cdot 7.5$ .

$X = [\begin{array}{c} 1.4 & - 2.8 \\ 2.5 & \frac{1}{3} \cdot - 0.6 \end{array}]$

Rearrange $\frac{1}{3} \cdot - 0.6$ .

$X = [\begin{array}{c} 1.4 & - 2.8 \\ 2.5 & - \frac{1}{5} \end{array}]$

Solve the Matrix Equation 3x-2[[1.5,-2.4],[3.6,-0.5]]=[[1.2,-3.6],[0.3,0.4]]

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