Sure! Let's go through the process of adding the given matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex] to find the elements [tex]\( C_{12} \)[/tex], [tex]\( C_{31} \)[/tex], and [tex]\( C_{22} \)[/tex] of the resultant matrix [tex]\( C \)[/tex].
The matrices given are:
[tex]\[ A = \begin{bmatrix}
16 & 9 \\
-3 & 0 \\
4 & -10
\end{bmatrix}
\][/tex]
[tex]\[ B = \begin{bmatrix}
-0.5 & 0 \\
5 & 8 \\
-3 & 14
\end{bmatrix}
\][/tex]
To find matrix [tex]\( C \)[/tex], we add the corresponding elements of matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
[tex]\[ C = A + B = \begin{bmatrix}
16 & 9 \\
-3 & 0 \\
4 & -10
\end{bmatrix}
+
\begin{bmatrix}
-0.5 & 0 \\
5 & 8 \\
-3 & 14
\end{bmatrix}
\][/tex]
Perform the element-wise addition:
[tex]\[ C = \begin{bmatrix}
16 + (-0.5) & 9 + 0 \\
-3 + 5 & 0 + 8 \\
4 + (-3) & -10 + 14
\end{bmatrix}
\][/tex]
Calculate each element:
[tex]\[ C = \begin{bmatrix}
15.5 & 9 \\
2 & 8 \\
1 & 4
\end{bmatrix}
\][/tex]
Now, the elements we need are:
- [tex]\( C_{12} \)[/tex] (element in the first row, second column)
- [tex]\( C_{31} \)[/tex] (element in the third row, first column)
- [tex]\( C_{22} \)[/tex] (element in the second row, second column)
Extracting these elements from matrix [tex]\( C \)[/tex]:
- [tex]\( C_{12} = 9 \)[/tex]
- [tex]\( C_{31} = 1 \)[/tex]
- [tex]\( C_{22} = 8 \)[/tex]
Thus, the values are:
[tex]\[ C_{12} = 9 \][/tex]
[tex]\[ C_{31} = 1 \][/tex]
[tex]\[ C_{22} = 8 \][/tex]
The correct choices are:
[tex]\[ c_{12} = 9 \][/tex]
[tex]\[ c_{31} = 1 \][/tex]
[tex]\[ c_{22} = 8 \][/tex]
So the result from running the code correctly gives us the answer [tex]\( c_{12} = 9 \)[/tex], [tex]\( c_{31} = 1 \)[/tex], and [tex]\( c_{22} = 8 \)[/tex].
