Question
If $\left[\begin{array}{ll}3 & 4 \\ 5 & 5\end{array}\right]=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ write down the values of $a, b, c$ and $d$
✓
Answer
Given
$
\begin{aligned}
& {\left[\begin{array}{ll}
3 & 4 \\
5 & 5
\end{array}\right]=\left[\begin{array}{ll}
a & b \\
c & d
\end{array}\right]\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right]} \\
& \Rightarrow\left[\begin{array}{ll}
3 & 4 \\
2 & 5
\end{array}\right]=\left[\begin{array}{ll}
a+0 & 0+b \\
c+0 & 0+d
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{ll}
3 & 4 \\
2 & 5
\end{array}\right]=\left[\begin{array}{ll}
a & b \\
c & d
\end{array}\right]
\end{aligned}
$
Comparing the corresponding elements
$
a=3, b=4, c=2, d=5 \text {. }
$
$
\begin{aligned}
& {\left[\begin{array}{ll}
3 & 4 \\
5 & 5
\end{array}\right]=\left[\begin{array}{ll}
a & b \\
c & d
\end{array}\right]\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right]} \\
& \Rightarrow\left[\begin{array}{ll}
3 & 4 \\
2 & 5
\end{array}\right]=\left[\begin{array}{ll}
a+0 & 0+b \\
c+0 & 0+d
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{ll}
3 & 4 \\
2 & 5
\end{array}\right]=\left[\begin{array}{ll}
a & b \\
c & d
\end{array}\right]
\end{aligned}
$
Comparing the corresponding elements
$
a=3, b=4, c=2, d=5 \text {. }
$
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