Solve the Matrix Equation 2x+[[2,5],[5,-4]]=[[2,-2],[3,5]]

$2 x + [\begin{array}{c} 2 & 5 \\ 5 & - 4 \end{array}] = [\begin{array}{c} 2 & - 2 \\ 3 & 5 \end{array}]$

Step 1

Subtract the matrix from both sides of the equation.

$2 X + [\begin{array}{c} 2 & 5 \\ 5 & - 4 \end{array}] - [\begin{array}{c} 2 & 5 \\ 5 & - 4 \end{array}] = [\begin{array}{c} 2 & - 2 \\ 3 & 5 \end{array}] - [\begin{array}{c} 2 & 5 \\ 5 & - 4 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 2 - 2 & 5 - 5 \\ 5 - 5 & - 4 - (- 4) \end{array}] + 2 X = [\begin{array}{c} 2 & - 2 \\ 3 & 5 \end{array}] - [\begin{array}{c} 2 & 5 \\ 5 & - 4 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 2 - 2 & 5 - 5 \\ 5 - 5 & - 4 - (- 4) \end{array}]$ .

Simplify $2 - 2$ .

$[\begin{array}{c} 0 & 5 - 5 \\ 5 - 5 & - 4 - (- 4) \end{array}] + 2 X = [\begin{array}{c} 2 & - 2 \\ 3 & 5 \end{array}] - [\begin{array}{c} 2 & 5 \\ 5 & - 4 \end{array}]$

Simplify $5 - 5$ .

$[\begin{array}{c} 0 & 0 \\ 5 - 5 & - 4 - (- 4) \end{array}] + 2 X = [\begin{array}{c} 2 & - 2 \\ 3 & 5 \end{array}] - [\begin{array}{c} 2 & 5 \\ 5 & - 4 \end{array}]$

Simplify $5 - 5$ .

$[\begin{array}{c} 0 & 0 \\ 0 & - 4 - (- 4) \end{array}] + 2 X = [\begin{array}{c} 2 & - 2 \\ 3 & 5 \end{array}] - [\begin{array}{c} 2 & 5 \\ 5 & - 4 \end{array}]$

Simplify $- 4 - (- 4)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + 2 X = [\begin{array}{c} 2 & - 2 \\ 3 & 5 \end{array}] - [\begin{array}{c} 2 & 5 \\ 5 & - 4 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + 2 X = [\begin{array}{c} 2 - 2 & - 2 - 5 \\ 3 - 5 & 5 - (- 4) \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 2 - 2 & - 2 - 5 \\ 3 - 5 & 5 - (- 4) \end{array}]$ .

Simplify $2 - 2$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + 2 X = [\begin{array}{c} 0 & - 2 - 5 \\ 3 - 5 & 5 - (- 4) \end{array}]$

Simplify $- 2 - 5$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + 2 X = [\begin{array}{c} 0 & - 7 \\ 3 - 5 & 5 - (- 4) \end{array}]$

Simplify $3 - 5$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + 2 X = [\begin{array}{c} 0 & - 7 \\ - 2 & 5 - (- 4) \end{array}]$

Simplify $5 - (- 4)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + 2 X = [\begin{array}{c} 0 & - 7 \\ - 2 & 9 \end{array}]$

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

$2 X = [\begin{array}{c} 0 & - 7 \\ - 2 & 9 \end{array}]$

Step 3

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

$\frac{1}{2} \cdot (2 X) = \frac{1}{2} \cdot [\begin{array}{c} 0 & - 7 \\ - 2 & 9 \end{array}]$

Step 4

Simplify both sides of the equation.

Cancel the common factor of $2$ .

Factor $2$ out of $2 X$ .

$\frac{1}{2} \cdot (2 (X)) = \frac{1}{2} \cdot [\begin{array}{c} 0 & - 7 \\ - 2 & 9 \end{array}]$

Cancel the common factor.

$\frac{1}{2} \cdot (2 X) = \frac{1}{2} \cdot [\begin{array}{c} 0 & - 7 \\ - 2 & 9 \end{array}]$

Rewrite the expression.

$X = \frac{1}{2} \cdot [\begin{array}{c} 0 & - 7 \\ - 2 & 9 \end{array}]$

Simplify the right side of the equation.

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

$X = [\begin{array}{c} \frac{1}{2} \cdot 0 & \frac{1}{2} \cdot - 7 \\ \frac{1}{2} \cdot - 2 & \frac{1}{2} \cdot 9 \end{array}]$

Simplify each element in the matrix.

Rearrange $\frac{1}{2} \cdot 0$ .

$X = [\begin{array}{c} 0 & \frac{1}{2} \cdot - 7 \\ \frac{1}{2} \cdot - 2 & \frac{1}{2} \cdot 9 \end{array}]$

Rearrange $\frac{1}{2} \cdot - 7$ .

$X = [\begin{array}{c} 0 & - \frac{7}{2} \\ \frac{1}{2} \cdot - 2 & \frac{1}{2} \cdot 9 \end{array}]$

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

$X = [\begin{array}{c} 0 & - \frac{7}{2} \\ - 1 & \frac{1}{2} \cdot 9 \end{array}]$

Rearrange $\frac{1}{2} \cdot 9$ .

$X = [\begin{array}{c} 0 & - \frac{7}{2} \\ - 1 & \frac{9}{2} \end{array}]$

Solve the Matrix Equation 2x+[[2,5],[5,-4]]=[[2,-2],[3,5]]

Related Questions

Support LCMGCF.com by disabling your adblocker.