Answer(a):
Order of matrix A = 3x3 {because number of rows=3, number of columns=3}
Order of matrix B = 3x3
Order of matrix C = 1x3
3A will be of order 3x3 because multiply by scalar doesn't change the order. Which is same as the order of matrix B.
So 3A+B is possible.
We simply multiply all elements of A with 3 and add them with corresponding elements of B.
[tex]3\begin{bmatrix}
2 & -1& 0\\
0 & 5& 0.3\\
1 & 4&10
\end{bmatrix}+
\begin{bmatrix}
5 & 0& 2\\
1 & -3& 9\\
2 & 0& 4
\end{bmatrix}= \begin{bmatrix}
11 & -3& 2\\
1 & 12& 9.9\\
5 & 12& 34
\end{bmatrix}[/tex]
Answer(b):
2B will be of order 3x3 because multiply by scalar doesn't change the order. Which is NOT same as the order of matrix C.
So 2B+C is NOT possible.
Answer(c):
CA is possible only if
number of columns of C = number of columns of A
3=3
which is true hence CA is possible.
[tex]\begin{bmatrix}
1 &3 &5
\end{bmatrix}
*\begin{bmatrix}
2 & -1& 0\\
0 & 5& 0.3\\
1 & 4&10
\end{bmatrix}=
\begin{bmatrix}
1*2+3*0+5*1 & 1*-1+3*5+5*4 & 1*0+3*0.3+5*10
\end{bmatrix}[/tex]
= [tex]\begin{bmatrix}
7 & 34& 50.9
\end{bmatrix}[/tex]
If the matrix is not visible properly then look at the attached picture.
