In Section 2.6, a linear transformation of y 1 = (3, 10, 20) to x 1 = (33, 17, −3) and of y 2 = (6, 14, 21) to x 2 = (41, 15, 1)’ was made using the matrix A The vectors of A were then standardized so...

In Section 2.6, a linear transformation of y₁
= (3, 10, 20) to x₁
= (33, 17, −3) and of y²
= (6, 14, 21) to x²
= (41, 15, 1)’ was made using the matrix A

The vectors of A were then standardized so that A’A = I to produce the orthogonal transformation of y₁
and y²
to

Respectively. Show that the squared distance between y₁
and y₂
is unchanged when the orthogonal transformation is made but not when the no northogonal transformation is made. That is, show that