Wat is de
omgekeerde
matrix van
  ? 		A.  \(\small\boldsymbol{\begin{bmatrix}0&\frac 12\\\frac 12&0\\\end{bmatrix} }\)
B.  \(\small\boldsymbol{\begin{bmatrix}0&-2\\-2&0\\\end{bmatrix} }\)
C.  \(\small\boldsymbol{\begin{bmatrix}0&-\frac 12\\-\frac 12&0\\\end{bmatrix} }\)
D.  \(\small\boldsymbol{\begin{bmatrix}2&0\\0&2\\\end{bmatrix} }\)
E.  \(\text{bestaat niet}\)
                 

[ 5-0453 - op net sinds 2.3.98-(E)-30.10.2023 ]

Translation in   E N G L I S H

The inverse of
the square matrix

is 		A.   \(\small\boldsymbol{\begin{bmatrix}0&\frac 12\\\frac 12&0\\\end{bmatrix} }\)
B.   \(\small\boldsymbol{\begin{bmatrix}0&-2\\-2&0\\\end{bmatrix} }\)
C.   \(\small\boldsymbol{\begin{bmatrix}0&-\frac 12\\-\frac 12&0\\\end{bmatrix} }\)
D.   \(\small\boldsymbol{\begin{bmatrix}2&0\\0&2\\\end{bmatrix} }\)
E.   \(\text{doesn't exist}\)

Oplossing - Solution

\( \begin{bmatrix}a&b\\c&d\end{bmatrix}^{-1}=\frac{1}{\begin{vmatrix} a & b \\ c & d \end{vmatrix}} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}\\ \text{op voorwaarde dat de determinant (noemer) niet nul is}\\ \begin{bmatrix} 0 & 2 \\ 2 & 0 \end{bmatrix}^{-1}=\frac{1}{\begin{vmatrix} 0 & 2 \\ 2 & 0 \end{vmatrix}} \begin{bmatrix} 0 & -2 \\ -2 & 0 \end{bmatrix}=\frac{1}{-4}\begin{bmatrix} 0 & -2 \\ -2 & 0 \end{bmatrix}=\begin{bmatrix} 0 & \frac 12 \\ \frac 12 & 0 \end{bmatrix}\\ \)