7 -2 2 Let A -2 7 2. The two eigenvalues of A are li = 3 and 2 27 X2 = 9. Find matrices D and P such that D=P-1 AP is an orthogonal diagonalization of A.
2 [ 2 ] Let 7 = -1 and 7 = 1 [ 1] (a) Find 7777, 7777, 777, and 777. (b) Find the distance between 7 and 7 by the la norm and the lo norm.
(1 point) Compute the determinant of the matrix -1 -2 -4 -6 -7 -7 7 7 A= 0 0 0 0 -4 -5 7 det(A) (1 point) Find the determinant of the matrix 6 A- 6 -9 -7 det(A) (1 point) Find the determinant of the matrix 2 2 -2 B= 1 -1 2 3 -2 det (B)
please answer with explanation
13) 13) x 2-4 -4 -2 4629-4 -2 y 7 -3 -7-7 4-2 -3 2-4-2 Y t) 2 1 10 x -10 B) A) O 10 C -10 O OC 10- D) C) o o o o
A-61 8 2 3-2 -3)+123)-7)+12(-2) -3)120-2 -7)+123) -3-6X-2)- -63 30 120)-7 12-2 -60)4-36x-2) 8-7) 123)8-3)+12-2 Viy that AB AC by simplitying Tyee an inleger or decimal for each matrix element) eick Check Answer
1 - 2y +32 3y + 2 r+y - 2 -10 7 = 7. 2. (5 points) Solve the above system using Cramer's Rule.
Differentiate the given function. f(t) = 247 [CLO 2.7 (12+72 - 2 + 7 2+7 - 2 + 7 (+2+7 -1 2+7
- 2 (3) (a) (7 points) Let w = I = + +7, y = cos(2), z = 4t. Use the Chain Rule to express or in terms of t. Then evaluate du at t= . (b) (7 points) Let w = 2+2y-42 es cos(3t), y e28sin(3t) and 2 = = 22 2r-y+3z) Use the Chain Rule to express and in terms of s and t. = 2 = ow os 8 åt
7. Let 7 = (1,-1,-2), ū = (2,-1,1) and = (2,-2,-4). Find: (a) *(-20) (4 pts) (b) (+37). ū (4 pts) (c) The vector of magnitude 5 that points in the same direction as (4 pts). (d) The angle between 7 and ū (4 pts). (e) Find Projz() (4 pts).
2. Consider Z7 Prove that the operation
on Z7 dened by [x]7
[y]7 =
[5xy]7 is well dened.
= 2. Consider Z- Prove that the operation ♡ on Z- defined by [2]7 0 [y]; [5xy]7 is well defined.