Answered

If one multiplies [tex]C[/tex] and [tex]B[/tex], what will be the value in the 3rd row and 2nd column of the resulting matrix? If the operation is not possible, then enter "not possible."

[tex]\[
A = \begin{bmatrix}
2 & -3 \\
-1 & 4
\end{bmatrix} \quad
B = \begin{bmatrix}
4 & -5 \\
1 & 3
\end{bmatrix} \quad
C = \begin{bmatrix}
2 & 12 \\
4 & 10 \\
6 & 8
\end{bmatrix}
\][/tex]

Answer: [tex]\square[/tex]



Answer :

GinnyAnswer
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]

Other Questions