Show that: 5&-1 6&7 2&1 3&4 2&1 3&4 5&-1 6&7 - Vidyadip

Question

Show that:
$\begin{bmatrix}5&-1\\6&7\end{bmatrix}\begin{bmatrix}2&1\\3&4\end{bmatrix}\neq\begin{bmatrix}2&1\\3&4\end{bmatrix}\begin{bmatrix}5&-1\\6&7\end{bmatrix}$

✓

Answer

$\text{L.H.S}=\begin{bmatrix}5&-1\\6&7\end{bmatrix}\begin{bmatrix}2&1\\3&4\end{bmatrix}$$=\begin{bmatrix}5(2) + (-1)3&5(1) + (-1)4\\6(2) + 7(3)&6(1) + 7(4)\end{bmatrix}$$ = \begin{bmatrix}7&1\\33&34\end{bmatrix} $
$\text{R.H.S} = \begin{bmatrix}2&1\\3&4\end{bmatrix}\begin{bmatrix}5&-1\\6&7\end{bmatrix} $$= \begin{bmatrix}2(5) + 1(6)&2(-1) + 1(7)\\3(5) + 4(6)&3(-1) + 4(7)\end{bmatrix} $$= \begin{bmatrix}16&5\\39&25\end{bmatrix} $
$\therefore \text{L.H.S.} \neq \text{R.H.S.}$

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