Question

The graph shows the result of matrix operation AB, where the pre-image has dashed lines. Which matrix could represent B?​

Answer 1

Matrix operations includes the addition, multiplication and subtraction of matrices

The correct option for the matrix that can be used to represent B is option D)

$D) = \left[\begin{array}{rrr}6&-3&-6\\5&9&5\end{array}\right]$

The reason the above option is correct is as follows:

From the graph, we have that the coordinates of the preimage are;

(-6, 5), (-3, 9), and (6, 5)

The coordinates of the preimage in matrix form is given as follows;

$\left[\begin{array}{rrr}6&-3&-6\\5&9&5\end{array}\right]$

The coordinates of the image are;

(-6, -5), (-3, -9), and (6, -5)

The coordinates of the image in matrix form is given as follows;

$\left[\begin{array}{rrr}6&-3&-6\\-5&-9&-5\end{array}\right]$

The above image matrix can be obtained from the primage matrix as follows:

$\left[\begin{array}{rrr}1&0\\0&-1\end{array}\right]\left[\begin{array}{rrr}6&-3&-6\\5&9&5\end{array}\right] = \left[\begin{array}{rrr}6&-3&-6\\-5&-9&-5\end{array}\right]$

Which is of the form AB = C

Where;

$A = \left[\begin{array}{rrr}1&0\\0&-1\end{array}\right]$

$B = \left[\begin{array}{rrr}6&-3&-6\\5&9&5\end{array}\right]$

$C = \left[\begin{array}{rrr}6&-3&-6\\-5&-9&-5\end{array}\right]$

Therefore, the matrix that could represent B is $\left[\begin{array}{rrr}6&-3&-6\\5&9&5\end{array}\right]$ which is option D)

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