Let A be a given matrix below. First, find the eigenvalues and their corresponding eigenspaces for the following matrices. Then, find an invertible matrix P and a diagonal matrix such that A = PDPâ’1. (a) [ 3 2 2 3 ]
(b) [ 1 â 1 2 â 1 ]
(c) [1 2 3 0 2 3 0 0 3]
(d) [3 1 1 1 3 1 1 1 3]

Ok a point t on a segment with endpoints d(1, 4) and f(7, 1) partitions the segment in a 2: 1 ratio. find t. you must show all work to receive credit.

Set up and solve a proportion for the following application problem. if 55 pounds of grass seed cover 404 square feet, how many pounds are needed for 7272 square feet?

Meghan has created a diagram of her city with her house, school, store, and gym identified. a. how far is it from the gym to the store? b. meghan also wants to walk to get some exercise, rather than going to the gym. she decides to walk along arc ab. how far will she walk? round to 3 decimal places.