Simplify the Matrix [[1,-4,3],[1,5,3],[0,-2,4]]^-1[[-11],[16],[-10]]

${[\begin{array}{c} 1 & - 4 & 3 \\ 1 & 5 & 3 \\ 0 & - 2 & 4 \end{array}]}^{- 1} [\begin{array}{c} - 11 \\ 16 \\ - 10 \end{array}]$

Step 1

Multiply each row in the first matrix by each column in the second matrix.

$[\begin{array}{c} 1 \cdot - 11 - 4 \cdot 16 + 3 \cdot - 10 \\ 1 \cdot - 11 + 5 \cdot 16 + 3 \cdot - 10 \\ 0 \cdot - 11 - 2 \cdot 16 + 4 \cdot - 10 \end{array}] {[\begin{array}{c} 1 & - 4 & 3 \\ 1 & 5 & 3 \\ 0 & - 2 & 4 \end{array}]}^{- 1} [\begin{array}{c} - 11 \\ 16 \\ - 10 \end{array}]$

Step 2

Simplify each element of the matrix by multiplying out all the expressions.

$[\begin{array}{c} - 105 \\ 39 \\ - 72 \end{array}] {[\begin{array}{c} 1 & - 4 & 3 \\ 1 & 5 & 3 \\ 0 & - 2 & 4 \end{array}]}^{- 1} [\begin{array}{c} - 11 \\ 16 \\ - 10 \end{array}]$

Step 3

Matrices can only be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix. The matrices cannot be multiplied.

$[\begin{array}{c} - 105 \\ 39 \\ - 72 \end{array}] {[\begin{array}{c} 1 & - 4 & 3 \\ 1 & 5 & 3 \\ 0 & - 2 & 4 \end{array}]}^{- 1} {[\begin{array}{c} - 11 \\ 16 \\ - 10 \end{array}]}^{- 1} [\begin{array}{c} - 11 \\ 16 \\ - 10 \end{array}]$

Simplify the Matrix [[1,-4,3],[1,5,3],[0,-2,4]]^-1[[-11],[16],[-10]]

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