Question

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

Answer 1

Answer:
`\left[\begin{array}{ccc}5\\-1\end{array}\right]`

Step-by-step explanation: I got this right on Edmentum.

Answer 2

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

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]`