Use a change of basis to represent a as the composite of a

Question

MATH 54 QUIZ 9-

1. Consider the matrix

Use a change of basis to represent A as the composite of a rotation and scaling transformation. In other words, find a real matrix

and invertible real matrix P such that A = PCP ^-1.

2. Consider the vectors

in R³. Find all vectors in R³ that are simultaneously orthogonal to v₁, v₂, v₃, v₄ with respect to the dot product.