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Given matrices
[tex]\[ X = \left[\begin{array}{ll}-1 & 0\end{array}\right] \][/tex]
and
[tex]\[ Y = \left[\begin{array}{l}-2 \\ -1\end{array}\right], \][/tex]
which of the following matrices is [tex]\( XY \)[/tex]?

A. [tex]\([-4]\)[/tex]

B. [tex]\([-3]\)[/tex]

C. [tex]\([-2]\)[/tex]

D. [tex]\([2]\)[/tex]

E. [tex]\([3]\)[/tex]



Answer :

GinnyAnswer
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.

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