a) Let F:R 2
→R 2
be the linear transformation corresponding to a reflection in the x-axis. Find the standard matrix for F. b) Let G:R 2
→R 3
be the linear transformation given by G( x
y
​
)= ⎝
⎛
​
x−y
2x+y
y
​
⎠
⎞
​
(i) Show that ker(G)={0}. (ii) Determine the nullity and the rank of G. (iii) Write down the standard matrix for G. (iv) Find the standard matrix for the linear transformation given by the reflection F, followed by the linear transformation G.