- #1

katie_3011

- 5

- 0

^{-1}=S

where F denotes the reflection in the x-axis

where S is the reflection in the line y=x

where R = R

_{[tex]\pi/4[/tex]}: R

^{2}[tex]\rightarrow[/tex] R

^{2}

3. An attempt

I have found that the standard matrix for R = [cos[tex]\theta[/tex] sin[tex]\theta[/tex]]

[sin[tex]\theta[/tex] cos[tex]\theta[/tex]]

So therefore, the inverse of R would be the same matrix.

The standard matrix for F = [1 0]

[0 -1]

When I multiplied the matrices together, I got a matrix [1 -1]

[1 1],

which does not equal S, which should be [0 1]

[1 0].

I have tried multiplying out the matrices a few times, and I'm pretty sure this is where my mistake is, but I'm not entirely sure how to multiply cos[tex]\theta[/tex] and sin[tex]\theta[/tex] with actual numbers.

Thanks in advance for your help