Question
If $P=\left[\begin{array}{ll}2 & 6 \\ 3 & 9\end{array}\right]$ and $Q=\left[\begin{array}{ll}3 & x \\ y & 2\end{array}\right]$ find $x$ and $y$ such that $P Q=$ null matrix
✓
Answer
$P Q=[(2,6),(3,9)][(3, x),(y, 2)]=[(6+6 y, 2 x+12),(9+9 y, 3 x+18)]^{\prime}$
PQ = Null matrix
∴ [(6 + 6y,2x + 12),(9 + 9y, 3x + 18)] = [(0,0),(0,0)]`
Comparing the corresponding elements we get
2x + 12 = 0
Therefore x = -6
6 + 6y = 0
Therefore y = -1
PQ = Null matrix
∴ [(6 + 6y,2x + 12),(9 + 9y, 3x + 18)] = [(0,0),(0,0)]`
Comparing the corresponding elements we get
2x + 12 = 0
Therefore x = -6
6 + 6y = 0
Therefore y = -1
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