MathAlgebraLinear algebraMatrices

Matrix inverse properties

Theory

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Calculate the following:

det⁡((0.0625−5−3−16−168−15080.25−1819−18−0.500−220−19−20−7000−120−15−2000000.050.25−0.0625000002.53000000−0.1)−1)\det{\Bigg(\begin{pmatrix} 0.0625 & -5 & -3 & -16 & -16 & 8 & -15 \\ 0 & 8 & 0.25 & -18 & 19 & -18 & -0.5 \\ 0 & 0 & -2 & 20 & -19 &-20 & -7 \\ 0 & 0 & 0 & -1 & 20 & -15 & -20 \\ 0 & 0 & 0 & 0 & 0.05 & 0.25 & -0.0625 \\ 0 & 0 & 0 & 0 & 0 & 2.5 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & -0.1 \end{pmatrix}^{-1}\Bigg)}

Write the determinant to the answer field.

Tip: Use the invertible matrix property for a determinant of a matrix inverse.

Tip: Notice the exact type of this big scary matrix.

Tip: Remember what the determinant of a triangular matrix is equal to, and calculate it.

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