To solve this problem, we need to determine if the matrix multiplication [tex]\( B \cdot A \)[/tex] is possible and then find the entry in row 1, column 2 of the resulting matrix.
1. Determine the dimensions of the matrices:
Matrix [tex]\( A \)[/tex] is a [tex]\( 2 \times 4 \)[/tex] matrix:
[tex]\[
A = \begin{pmatrix}
4 & 2 & 3 & 6 \\
4 & 1 & 0 & 3 \\
\end{pmatrix}
\][/tex]
Matrix [tex]\( B \)[/tex] is a [tex]\( 3 \times 4 \)[/tex] matrix:
[tex]\[
B = \begin{pmatrix}
5 & 4 & 6 & 0 \\
1 & 1 & 2 & 0 \\
3 & 3 & 0 & 1 \\
\end{pmatrix}
\][/tex]
2. Check if the matrix multiplication [tex]\( B \cdot A \)[/tex] is possible:
For matrix multiplication [tex]\( B \cdot A \)[/tex] to be defined, the number of columns in [tex]\( B \)[/tex] must equal the number of rows in [tex]\( A \)[/tex].
- Matrix [tex]\( B \)[/tex] has 4 columns.
- Matrix [tex]\( A \)[/tex] has 2 rows.
Since the number of columns in [tex]\( B \)[/tex] (which is 4) does not match the number of rows in [tex]\( A \)[/tex] (which is 2), the matrix multiplication [tex]\( B \cdot A \)[/tex] is not possible.
Therefore, the problem cannot be solved as [tex]\( B \cdot A \)[/tex] cannot be done.
The final answer is:
[tex]\[ \text{can't be done} \][/tex]
