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Select the best answer for the question.

[tex]\[ B=\left[\begin{array}{cc} 2 & 8 \\ 6 & 3 \end{array}\right] \quad A=\left[\begin{array}{cc} 3 & 0 \\ 2 & -1 \end{array}\right] \][/tex]

20. What is [tex]\( BA \)[/tex]?

A. [tex]\(\left[\begin{array}{cc} 22 & -8 \\ 3 & -3 \end{array}\right]\)[/tex]

B. [tex]\(\left[\begin{array}{cc} 6.2 & 3 \\ 12.2 & -18 \end{array}\right]\)[/tex]

C. [tex]\(\left[\begin{array}{cc} 6 & 24 \\ 3.4 & 13 \end{array}\right]\)[/tex]

D. [tex]\(\left[\begin{array}{cc} 22 & -8 \\ 7.8 & -3 \end{array}\right]\)[/tex]



Answer :

To solve for the product [tex]\( BA \)[/tex] where
[tex]\[ B = \begin{pmatrix} 2 & 8 \\ 6 & 3 \end{pmatrix} \][/tex]
and
[tex]\[ A = \begin{pmatrix} 3 & 0 \\ 2 & -1 \end{pmatrix} \][/tex]
we need to perform matrix multiplication.

Given that the result of the matrix multiplication [tex]\( BA \)[/tex] is:
[tex]\[ BA = \begin{pmatrix} 22 & -8 \\ 24 & -3 \end{pmatrix} \][/tex]

Let's now match this result with the provided options:

A. [tex]\(\begin{pmatrix} 22 & -8 \\ 3 & -3 \end{pmatrix}\)[/tex]

B. [tex]\(\begin{pmatrix} 6.2 & 3 \\ 12.2 & -18 \end{pmatrix}\)[/tex]

C. [tex]\(\begin{pmatrix} 6 & 24 \\ 3.4 & 13 \end{pmatrix}\)[/tex]

D. [tex]\(\begin{pmatrix} 22 & -8 \\ 7.8 & -3 \end{pmatrix}\)[/tex]

None of these match the correct result exactly.

Given the provided choices, none of them correctly match the solution that we have for the matrix [tex]\( BA \)[/tex].

Hence, there appears to be an error in the provided answer choices. If forced to select the closest, we'd select [tex]\( B \)[/tex], which partially matches one element. But none fully match, suggesting a possible issue in the formulation of the options.