Question

each column of the matrix ( a=left\begin{array}{llll}1 & 6 & 6 & 1 \\ 1 & 1 & 5 & 5end{array}
ight ) represents a vertex of a rectangle on the coordinate plane. if fan scales the rectangle by finding ( 4 a ), what are the vertices of the scaled rectangle?
( (4,4),(24,4),(24,20),(4,20) )
( (5,5),(10,5),(10,9),(5,9) )
( (4,4),(6,1),(6,5),(1,5) )
( (5,5),(6,1),(6,5),(4,20) )

Explanation:

Step1: Matrix - scalar multiplication

Multiply each element of matrix \(A=

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

\) by scalar \(4\).
For the first row: \(4\times1 = 4\), \(4\times6=24\), \(4\times6 = 24\), \(4\times1=4\).
For the second row: \(4\times1 = 4\), \(4\times1=4\), \(4\times5 = 20\), \(4\times5=20\).

Step2: Form vertices

The columns of \(4A=

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

\) give the vertices \((4,4)\), \((24,4)\), \((24,20)\), \((4,20)\) (column - wise as \((x,y)\) pairs).

Answer:

A. (4, 4), (24, 4), (24, 20), (4, 20)