To solve this problem, follow these steps:
1. Matrix [tex]\( A \)[/tex] Representation:
We need to work with the matrix [tex]\( A \)[/tex]:
[tex]\[
A = \left[\begin{array}{ccc}
1 & 2 & -4 \\
0 & 3 & -1
\end{array}\right]
\][/tex]
2. Scaling the Matrix [tex]\( A \)[/tex] by 4:
To compute [tex]\( 4A \)[/tex], we multiply each element of the matrix [tex]\( A \)[/tex] by 4. So, we calculate each element as follows:
[tex]\[
4A = 4 \times \left[\begin{array}{ccc}
1 & 2 & -4 \\
0 & 3 & -1
\end{array}\right] = \left[\begin{array}{ccc}
4 \times 1 & 4 \times 2 & 4 \times -4 \\
4 \times 0 & 4 \times 3 & 4 \times -1
\end{array}\right]
\][/tex]
Performing the multiplications:
[tex]\[
4A = \left[\begin{array}{ccc}
4 & 8 & -16 \\
0 & 12 & -4
\end{array}\right]
\][/tex]
3. Extracting the Particular Element:
We are asked to find the element in row 2, column 3 of the matrix [tex]\( 4A \)[/tex]. From the matrix computed:
[tex]\[
4A = \left[\begin{array}{ccc}
4 & 8 & -16 \\
0 & 12 & -4
\end{array}\right]
\][/tex]
Look at the second row:
[tex]\[
\left[0, 12, -4\right]
\][/tex]
The element in column 3 of this row is [tex]\( -4 \)[/tex].
So, the element in row 2, column 3 of [tex]\( 4A \)[/tex] is:
[tex]\[
-4
\][/tex]
