Question

2020-12-31

asked 2020-11-17

asked 2020-11-01

asked 2021-01-31

asked 2020-10-18

Given the elow bases for \(R^2\) and the point at the specified coordinate in the standard basis as below, (40 points)

\((B1 = \left\{ (1, 0), (0, 1) \right\} \)&

\( B2 = (1, 2), (2, -1) \}\)(1, 7) = \(3^* (1, 2) - (2, 1)\)

\(B2 = (1, 1), (-1, 1) (3, 7 = 5^* (1, 1) + 2^* (-1,1)\)

\(B2 = (1, 2), (2, 1) \ \ \ (0, 3) = 2^* (1, 2) -2^* (2, 1)\)

\((8,10) = 4^* (1, 2) + 2^* (2, 1)\)

B2 = (1, 2), (-2, 1) (0, 5) =

(1, 7) =

a. Use graph technique to find the coordinate in the second basis. (10 points) b. Show that each basis is orthogonal. (5 points) c. Determine if each basis is normal. (5 points) d. Find the transition matrix from the standard basis to the alternate basis. (15 points)