Let's find the product of matrices [tex]\(X\)[/tex] and [tex]\(Y\)[/tex]. The matrices are as follows:
[tex]\[
X = \left[\begin{array}{cc}-1 & 0\end{array}\right]
\][/tex]
[tex]\[
Y = \left[\begin{array}{c}-2 \\ -1\end{array}\right]
\][/tex]
To multiply a 1×2 matrix by a 2×1 matrix, we perform the following steps:
1. Multiply the elements of the first row of [tex]\(X\)[/tex] by the corresponding elements of the first column of [tex]\(Y\)[/tex].
2. Sum these products to get the resulting element of the product matrix.
Here is the multiplication in detail:
[tex]\[ \text{Element 1,1 of the product} = (-1 \cdot -2) + (0 \cdot -1) \][/tex]
Perform the calculations:
[tex]\[ (-1 \cdot -2) = 2 \][/tex]
[tex]\[ (0 \cdot -1) = 0 \][/tex]
Sum these results:
[tex]\[ 2 + 0 = 2 \][/tex]
Thus, the product [tex]\(XY\)[/tex] is:
[tex]\[
XY = [2]
\][/tex]
Comparing this result to the given options:
A. [tex]\([-4]\)[/tex]
B. [tex]\([-3]\)[/tex]
C. [tex]\([-2]\)[/tex]
D. [tex]\([2]\)[/tex]
E. [tex]\([3]\)[/tex]
The correct answer is [tex]\( \mathbf{[2]} \)[/tex], which matches option D.
