To understand if multiplying matrices [tex]\( B \)[/tex] and [tex]\( C \)[/tex] is possible, let's first review their dimensions:
1. Matrix [tex]\( B \)[/tex] is a [tex]\( 2 \times 2 \)[/tex] matrix:
[tex]\[ B = \left[\begin{array}{cc}
4 & -5 \\
1 & 3
\end{array}\right] \][/tex]
2. Matrix [tex]\( C \)[/tex] is a [tex]\( 3 \times 2 \)[/tex] matrix:
[tex]\[ C = \left[\begin{array}{cc}
2 & 12 \\
4 & 10 \\
6 & 8
\end{array}\right] \][/tex]
In matrix multiplication, the number of columns in the first matrix must match the number of rows in the second matrix to perform the multiplication.
For matrices [tex]\( B \)[/tex] and [tex]\( C \)[/tex]:
- [tex]\( B \)[/tex] has 2 columns.
- [tex]\( C \)[/tex] has 3 rows.
Since the number of columns in [tex]\( B \)[/tex] (2) does not equal the number of rows in [tex]\( C \)[/tex] (3), matrix [tex]\( B \)[/tex] cannot be multiplied by matrix [tex]\( C \)[/tex]. Therefore, the operation is not possible.
Thus, the answer is:
[tex]\[ \text{not possible} \][/tex]
