Question

Which vector matrix represents the reflection of the vector <-1,5> across the line x = y

Answer 1

Answer:

$V = \left[\begin{array}{ccc}5&-1\end{array}\right]$

Step-by-step explanation:

We want to reflect this 2x1 vector on the line y = x.

To make this reflection we must use the following matrix:

$R=\left[\begin{array}{cc}0&1\\1&0\\\end{array}\right]$

Where R is known as the reflection matrix on the line x = y

Now perform the product of the vector <-1,5> x R.

$\left[\begin{array}{ccc}-1\\5\end{array}\right]x\left[\begin{array}{ccc}0&1\\1&0\end{array}\right]\\\\\\\left[\begin{array}{ccc}-1(0) +5(1)&-1(1)+5(0)\end{array}\right]\\\\\\\left[\begin{array}{ccc}5&-1\end{array}\right]$

The vector matrix that represents the reflection of the vector <-1,5> across the line x = y is:

$V = \left[\begin{array}{ccc}5&-1\end{array}\right]$