Solve the Matrix Equation [[7,8],[9,10],[11,12]]-P=[[0,0],[0,0],[0,0]]

$[\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{array}] - P = [\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}]$

Step 1

Subtract the matrix from both sides of the equation.

$[\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{array}] - X - [\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{array}] = [\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - [\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 7 - 7 & 8 - 8 \\ 9 - 9 & 10 - 10 \\ 11 - 11 & 12 - 12 \end{array}] - X = [\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - [\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 7 - 7 & 8 - 8 \\ 9 - 9 & 10 - 10 \\ 11 - 11 & 12 - 12 \end{array}]$ .

Simplify $7 - 7$ .

$[\begin{array}{c} 0 & 8 - 8 \\ 9 - 9 & 10 - 10 \\ 11 - 11 & 12 - 12 \end{array}] - X = [\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - [\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{array}]$

Simplify $8 - 8$ .

$[\begin{array}{c} 0 & 0 \\ 9 - 9 & 10 - 10 \\ 11 - 11 & 12 - 12 \end{array}] - X = [\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - [\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{array}]$

Simplify $9 - 9$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 10 - 10 \\ 11 - 11 & 12 - 12 \end{array}] - X = [\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - [\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{array}]$

Simplify $10 - 10$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 11 - 11 & 12 - 12 \end{array}] - X = [\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - [\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{array}]$

Simplify $11 - 11$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 12 - 12 \end{array}] - X = [\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - [\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{array}]$

Simplify $12 - 12$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - [\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} 0 - 7 & 0 - 8 \\ 0 - 9 & 0 - 10 \\ 0 - 11 & 0 - 12 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 0 - 7 & 0 - 8 \\ 0 - 9 & 0 - 10 \\ 0 - 11 & 0 - 12 \end{array}]$ .

Simplify $0 - 7$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} - 7 & 0 - 8 \\ 0 - 9 & 0 - 10 \\ 0 - 11 & 0 - 12 \end{array}]$

Simplify $0 - 8$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} - 7 & - 8 \\ 0 - 9 & 0 - 10 \\ 0 - 11 & 0 - 12 \end{array}]$

Simplify $0 - 9$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} - 7 & - 8 \\ - 9 & 0 - 10 \\ 0 - 11 & 0 - 12 \end{array}]$

Simplify $0 - 10$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} - 7 & - 8 \\ - 9 & - 10 \\ 0 - 11 & 0 - 12 \end{array}]$

Simplify $0 - 11$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} - 7 & - 8 \\ - 9 & - 10 \\ - 11 & 0 - 12 \end{array}]$

Simplify $0 - 12$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] - X = [\begin{array}{c} - 7 & - 8 \\ - 9 & - 10 \\ - 11 & - 12 \end{array}]$

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

$- X = [\begin{array}{c} - 7 & - 8 \\ - 9 & - 10 \\ - 11 & - 12 \end{array}]$

Step 3

Multiply both sides of the equation by $- 1$ .

$- 1 \cdot (- X) = - 1 \cdot [\begin{array}{c} - 7 & - 8 \\ - 9 & - 10 \\ - 11 & - 12 \end{array}]$

Step 4

Simplify both sides of the equation.

Multiply $- 1 (- X)$ .

Multiply $- 1$ by $- 1$ .

$1 X = - 1 \cdot [\begin{array}{c} - 7 & - 8 \\ - 9 & - 10 \\ - 11 & - 12 \end{array}]$

Multiply $X$ by $1$ .

$X = - 1 \cdot [\begin{array}{c} - 7 & - 8 \\ - 9 & - 10 \\ - 11 & - 12 \end{array}]$

Simplify the right side of the equation.

Multiply $- 1$ by each element of the matrix.

$X = [\begin{array}{c} - 1 \cdot - 7 & - 1 \cdot - 8 \\ - 1 \cdot - 9 & - 1 \cdot - 10 \\ - 1 \cdot - 11 & - 1 \cdot - 12 \end{array}]$

Simplify each element in the matrix.

Rearrange $- 1 \cdot - 7$ .

$X = [\begin{array}{c} 7 & - 1 \cdot - 8 \\ - 1 \cdot - 9 & - 1 \cdot - 10 \\ - 1 \cdot - 11 & - 1 \cdot - 12 \end{array}]$

Rearrange $- 1 \cdot - 8$ .

$X = [\begin{array}{c} 7 & 8 \\ - 1 \cdot - 9 & - 1 \cdot - 10 \\ - 1 \cdot - 11 & - 1 \cdot - 12 \end{array}]$

Rearrange $- 1 \cdot - 9$ .

$X = [\begin{array}{c} 7 & 8 \\ 9 & - 1 \cdot - 10 \\ - 1 \cdot - 11 & - 1 \cdot - 12 \end{array}]$

Rearrange $- 1 \cdot - 10$ .

$X = [\begin{array}{c} 7 & 8 \\ 9 & 10 \\ - 1 \cdot - 11 & - 1 \cdot - 12 \end{array}]$

Rearrange $- 1 \cdot - 11$ .

$X = [\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & - 1 \cdot - 12 \end{array}]$

Rearrange $- 1 \cdot - 12$ .

$X = [\begin{array}{c} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{array}]$

Solve the Matrix Equation [[7,8],[9,10],[11,12]]-P=[[0,0],[0,0],[0,0]]

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