A First Course in Linear Algebra · Problem MISLE.C26

Matrices — Robert Beezer

Mathematics — Linear Algebra · matrix-inverse-computation

Problem

Let D=[1−13−21−23−5301−14−22−14−104105−25]D = \begin{bmatrix} 1 & -1 & 3 & -2 & 1 \\ -2 & 3 & -5 & 3 & 0 \\ 1 & -1 & 4 & -2 & 2 \\ -1 & 4 & -1 & 0 & 4 \\ 1 & 0 & 5 & -2 & 5 \end{bmatrix} Compute the inverse of DD, D−1D^{-1}, by forming the 5×105 \times 10 matrix [D∣I5][D \mid I_5] and row-reducing (Theorem CINM). Then use a calculator to compute D−1D^{-1} directly.

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