QQuestion
A = \begin{bmatrix}x & 0 \\ 1 & 1\end{bmatrix}, B = \begin{bmatrix}4 & 0 \\ y & 1\end{bmatrix} and C = \begin{bmatrix}4 & 0 \\ x & 1\end{bmatrix}.
Find the values of x and y, if AB = C.
✓Answer
Given, AB = C.
\begin{bmatrix}x & 0 \\ 1 & 1\end{bmatrix}\begin{bmatrix}4 & 0 \\ y & 1\end{bmatrix}=\begin{bmatrix}4 & 0 \\ x & 1\end{bmatrix}Multiplying the matrices:
\begin{bmatrix}(x\times4)+(0\times y) & (x\times0)+(0\times1) \\ (1\times4)+(1\times y) & (1\times0)+(1\times1)\end{bmatrix}=\begin{bmatrix}4 & 0 \\ x & 1\end{bmatrix} \begin{bmatrix}4x & 0 \\ 4+y & 1\end{bmatrix}=\begin{bmatrix}4 & 0 \\ x & 1\end{bmatrix}Equating corresponding elements:
4x = 4
⇒ x = 1
Also, 4 + y = x
⇒ 4 + y = 1
⇒ y = 1 − 4
⇒ y = −3
Therefore, x = 1 and y = −3.
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