A First Course in Linear Algebra · Problem MISLE.C27

Matrices — Robert Beezer

Mathematics — Linear Algebra · matrix-inverse-computation

Problem

Let

E = \begin{bmatrix} 1 & -1 & 3 & -2 & 1 \\ -2 & 3 & -5 & 3 & -1 \\ 1 & -1 & 4 & -2 & 2 \\ -1 & 4 & -1 & 0 & 2 \\ 1 & 0 & 5 & -2 & 4 \end{bmatrix}

Compute the inverse of

E

E^{-1}

, by forming the

5 \times 10

matrix

[E \mid I_5]

and row-reducing (Theorem CINM). Then use a calculator to compute

E^{-1}

directly.