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Let A begin bmatrix 2 amp 3 0 amp - 2 4 amp 5 e... - SS3 Mathematics Matrices and Determinants Question

Let \(A = \begin{bmatrix} 2 & 3 \\ 0 & - 2 \\ 4 & 5 \\ \end{bmatrix}\) and \(B = \begin{bmatrix} 1 & 3 & 2 \\ - 1 & 0 & 6 \\ \end{bmatrix}\). Find \(BA\)

A

\(\begin{bmatrix} 10 & 7 \\ 22 & 27 \\ \end{bmatrix}\)

B

\(\begin{bmatrix} 3 & 6 \\ 3 & 0 \\ \end{bmatrix}\)

C

\(\begin{bmatrix} 5 & 12 \\ 11 & 5 \\ \end{bmatrix}\)

D

\(\begin{bmatrix} 9 & 0 \\ - 1 & 5 \\ \end{bmatrix}\)

correct option: a

\(A = \begin{bmatrix} 2 & 3 \\ 0 & - 2 \\ 4 & 5 \\ \end{bmatrix}\) and \(B = \begin{bmatrix} 1 & 3 & 2 \\ - 1 & 0 & 6 \\ \end{bmatrix}\)

\(BA = \begin{bmatrix} 1 & 3 & 2 \\ - 1 & 0 & 6 \\ \end{bmatrix}\begin{bmatrix} 2 & 3 \\ 0 & - 2 \\ 4 & 5 \\ \end{bmatrix}\)

\[c_{11} = 1(2) + 3(0) + 2(4) = 2 + 0 + 8 = 10\]

\[c_{12} = 1(3) + 3( - 2) + 2(5) = 3 - 6 + 10 = 7\]

\[c_{21} = - 1(2) + 0(0) + 6(4) = - 2 + 0 + 24 = 22\]

\[c_{22} = - 1(3) + 0( - 2) + 6(5) = - 3 + 0 + 30 = 27\]

\(BA = \begin{bmatrix} 10 & 7 \\ 22 & 27 \\ \end{bmatrix}\)

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