MATH 54 QUIZ 9-
1. Consider the matrix
![2454_Figure.png](https://secure.tutorsglobe.com/CMSImages/2454_Figure.png)
Use a change of basis to represent A as the composite of a rotation and scaling transformation. In other words, find a real matrix
![1781_Figure1.png](https://secure.tutorsglobe.com/CMSImages/1781_Figure1.png)
and invertible real matrix P such that A = PCP -1.
2. Consider the vectors
![2436_Figure2.png](https://secure.tutorsglobe.com/CMSImages/2436_Figure2.png)
in R3. Find all vectors in R3 that are simultaneously orthogonal to v1, v2, v3, v4 with respect to the dot product.