Solve the Matrix Equation [[d,3],[e,1]]+[[2,f],[2,g]]=[[5,3],[1,2]]

$[\begin{array}{c} d & 3 \\ e & 1 \end{array}] + [\begin{array}{c} 2 & f \\ 2 & g \end{array}] = [\begin{array}{c} 5 & 3 \\ 1 & 2 \end{array}]$

Step 1

Add $X$ and $X$ .

$2 X = [\begin{array}{c} 5 & 3 \\ 1 & 2 \end{array}]$

Step 2

Multiply both sides of the equation by $\frac{1}{2}$ .

$\frac{1}{2} \cdot (2 X) = \frac{1}{2} \cdot [\begin{array}{c} 5 & 3 \\ 1 & 2 \end{array}]$

Step 3

Simplify both sides of the equation.

Cancel the common factor of $2$ .

Factor $2$ out of $2 X$ .

$\frac{1}{2} \cdot (2 (X)) = \frac{1}{2} \cdot [\begin{array}{c} 5 & 3 \\ 1 & 2 \end{array}]$

Cancel the common factor.

$\frac{1}{2} \cdot (2 X) = \frac{1}{2} \cdot [\begin{array}{c} 5 & 3 \\ 1 & 2 \end{array}]$

Rewrite the expression.

$X = \frac{1}{2} \cdot [\begin{array}{c} 5 & 3 \\ 1 & 2 \end{array}]$

Simplify the right side of the equation.

Multiply $\frac{1}{2}$ by each element of the matrix.

$X = [\begin{array}{c} \frac{1}{2} \cdot 5 & \frac{1}{2} \cdot 3 \\ \frac{1}{2} \cdot 1 & \frac{1}{2} \cdot 2 \end{array}]$

Simplify each element in the matrix.

Rearrange $\frac{1}{2} \cdot 5$ .

$X = [\begin{array}{c} \frac{5}{2} & \frac{1}{2} \cdot 3 \\ \frac{1}{2} \cdot 1 & \frac{1}{2} \cdot 2 \end{array}]$

Rearrange $\frac{1}{2} \cdot 3$ .

$X = [\begin{array}{c} \frac{5}{2} & \frac{3}{2} \\ \frac{1}{2} \cdot 1 & \frac{1}{2} \cdot 2 \end{array}]$

Rearrange $\frac{1}{2} \cdot 1$ .

$X = [\begin{array}{c} \frac{5}{2} & \frac{3}{2} \\ \frac{1}{2} & \frac{1}{2} \cdot 2 \end{array}]$

Rearrange $\frac{1}{2} \cdot 2$ .

$X = [\begin{array}{c} \frac{5}{2} & \frac{3}{2} \\ \frac{1}{2} & 1 \end{array}]$