Suppose we have $3$ data points in $2$D space: $(1,1),(2,2)$ and $(3,3)($a$)$ What is the principle component of $(1,1)?($b$)$ If we want to project the original data points into $1$D space by principle component you choose, what is the variance of the projected data? $($c$)$ For the projected data in $($b$),$ now iff we represent them in the original $2$D space, what is the reconstruction error?