Question

each column of the matrix ( a=\begin{bmatrix}1&6&6&1\\1&1&5&5end{bmatrix} ) represents a vertex of a rectangle on the coordinate plane. if fan scalesthe rectangle by finding ( 4a ), what are the vertices of the scaled rectangle?
( (4,4),(24,4),(24,20),(4,20) )
( (4,4),(6,1),(6,5),(1,5) )
( (5,5),(6,1),(6,5),(4,20) )

Explanation:

Step1: Multiply each element of matrix \(A\) by \(4\)

Given \(A=

$$\begin{bmatrix}1&6&6&1\\1&1&5&5\end{bmatrix}$$

\), then \(4A = 4\times

$$\begin{bmatrix}1&6&6&1\\1&1&5&5\end{bmatrix}$$

=

$$\begin{bmatrix}4\times1&4\times6&4\times6&4\times1\\4\times1&4\times1&4\times5&4\times5\end{bmatrix}$$

\)

Step2: Calculate each element

\(

$$\begin{bmatrix}4&24&24&4\\4&4&20&20\end{bmatrix}$$

\)

The vertices of the rectangle are \((4,4)\), \((24,4)\), \((24,20)\), \((4,20)\) (written as \((x,y)\) pairs from the columns of the matrix \(4A\))

Answer:

\((4,4)\), \((24,4)\), \((24,20)\), \((4,20)\) (corresponds to the first option)