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Matrix [tex]\( A=\left[\begin{array}{cc}6 & -12 \\ 4 & 8\end{array}\right] \)[/tex].

What is matrix [tex]\( X \)[/tex] if [tex]\( \frac{1}{2} X = A \)[/tex]?

A. [tex]\(\left[\begin{array}{cc}3 & -6 \\ 2 & 4\end{array}\right]\)[/tex]

B. [tex]\(\left[\begin{array}{cc}5.5 & -12.5 \\ 3.5 & 7.5\end{array}\right]\)[/tex]

C. [tex]\(\left[\begin{array}{cc}6.5 & -11.5 \\ 4.5 & 8.5\end{array}\right]\)[/tex]

D. [tex]\(\left[\begin{array}{cc}12 & -24 \\ 8 & 16\end{array}\right]\)[/tex]



Answer :

GinnyAnswer
To find matrix [tex]\( X \)[/tex], given [tex]\( \frac{1}{2} X = A \)[/tex], we need to isolate [tex]\( X \)[/tex]. We can do this by multiplying both sides of the equation by 2:

[tex]\[ 2 \left( \frac{1}{2} X \right) = 2A \][/tex]

This simplifies to:

[tex]\[ X = 2A \][/tex]

Given matrix [tex]\( A \)[/tex]:

[tex]\[ A = \left[\begin{array}{cc} 6 & -12 \\ 4 & 8 \end{array}\right] \][/tex]

We multiply each element of matrix [tex]\( A \)[/tex] by 2 to find matrix [tex]\( X \)[/tex]:

[tex]\[ X = 2 \times \left[\begin{array}{cc} 6 & -12 \\ 4 & 8 \end{array}\right] = \left[\begin{array}{cc} 2 \times 6 & 2 \times -12 \\ 2 \times 4 & 2 \times 8 \end{array}\right] \][/tex]

This results in:

[tex]\[ X = \left[\begin{array}{cc} 12 & -24 \\ 8 & 16 \end{array}\right] \][/tex]

We now compare this result with the provided options:

1. [tex]\(\left[\begin{array}{cc}3 & -6 \\ 2 & 4\end{array}\right]\)[/tex]
2. [tex]\(\left[\begin{array}{cc}5.5 & -12.5 \\ 3.5 & 7.5\end{array}\right]\)[/tex]
3. [tex]\(\left[\begin{array}{cc}6.5 & -11.5 \\ 4.5 & 8.5\end{array}\right]\)[/tex]
4. [tex]\(\left[\begin{array}{cc}12 & -24 \\ 8 & 16\end{array}\right]\)[/tex]

The correct matrix [tex]\( X \)[/tex] matches option 4:

[tex]\[ \left[\begin{array}{cc} 12 & -24 \\ 8 & 16 \end{array}\right] \][/tex]

Thus, the correct answer is option 4.

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