Answer:
Option: B is the correct
Step-by-step explanation:
Step-by-step explanation:
We are given two matrices A and B as follows:
\begin{gathered}A=\left[\begin{array}{ccc}3&0\\2&-1\end{array}\right]\end{gathered}
A=[
3
2
0
−1
]
and
\begin{gathered}B=\left[\begin{array}{ccc}2&8\\0.6&3\end{array}\right]\end{gathered}
B=[
2
0.6
8
3
]
We know that the multiplication of two matrices of the type:
\begin{gathered}A=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]\end{gathered}
A=[
a
c
b
d
]
and
\begin{gathered}B=\left[\begin{array}{ccc}a'&b'\\c'&d'\end{array}\right]\end{gathered}
B=[
a
′
c
′
b
′
d
′
]
is given by:
\begin{gathered}AB=\left[\begin{array}{ccc}aa'+bc'&ab'+bd'\\ca'+dc'&cb'+dd'\end{array}\right]\end{gathered}
AB=[
aa
′
+bc
′
ca
′
+dc
′
ab
′
+bd
′
cb
′
+dd
′
]
Hence, here we have:
\begin{gathered}AB=\left[\begin{array}{ccc}3\times 2+0\times 0.6&3\times 8+0\times 3\\2\times 2+(-1)\times 0.6&2\times 8+(-1)\times 3\end{array}\right]\end{gathered}
AB=[
3×2+0×0.6
2×2+(−1)×0.6
3×8+0×3
2×8+(−1)×3
]
i.e.
\begin{gathered}AB=\left[\begin{array}{ccc}6+0&24+0\\4-0.6&16-3\end{array}\right]\end{gathered}
AB=[
6+0
4−0.6
24+0
16−3
]
i.e.
\begin{gathered}AB=\left[\begin{array}{ccc}6&24\\3.4&13\end{array}\right]\end{gathered}
AB=[
6
3.4
24
13
]
