
mixture 3. Let 0 0 1 0 1 2 1 2 Z loo 4 X 0 A= and B = Y 4 1 (a) Compute the determinants of the following matrices: A, B, AB, 5AB, and (AB) (b) Compute the inverse of A. X = 3 Y = 3 Z = 6
Comoute the determinant of the matrix 1 -2 4 5 028-4 0 0 3 7 Loo 04 where I denoles the transpose of matrix
2. Show that the closed ball of radius 1 centered at 0 in Loo cannot be covered Hint: Think about the result by finitely many closed balls of radius of Problem 14 in Section 7.1.)
2. Show that the closed ball of radius 1 centered at 0 in Loo cannot be covered Hint: Think about the result by finitely many closed balls of radius of Problem 14 in Section 7.1.)
Exercise 1 Let 1 1 2 4 A= -16 2 5 1 2 - 1 0 2 3 loo-1/ and B 1 2 (1 1 -3 -1 2 2 0 / (1) Compute det A. 3 (2 .-1)-(3.0) = 1.(-2) - (0) = -2 (2) Evaluate : det (+(2(342)*)*") (3) Compute det B.
4. (3 points) Let ſi 2 1] A= 0 4 3 [1 2 2 Compute the third column of A-1 by solving the equation Ax = es, where ez = 0 Hint: Use Cramar's rule to solve the equation, noticing that the third column of A-' is given by the solution of the above equation. In fact there is nothing special about A-1, the third column of any 3 x 3 matrix B is given by the product Bez. Can...
Compute the indicated product. 2 -1 0 4 5 2 2 2 3 -3 0 1 0 -1 0 =
Problem #1 Let A= [3 4 37 5 7 2 To oil a) Find the adj of A b) A
QUESTION 1 Compute the determinant of A by any method where 1 4 -2 2 A= 2 0 3 0 2 0 1 - 2 | -1 -2 1 1 Attach File Browse My Computer Browse Content Collection
5. (12 pts) Let A= 4 -1 2 -1 3 -3 2 0 2 1 Find A-? using the formula A-1 adj(A). det(A)
(1 point) Find the least-squares solution x* of the system [10] 0 1 x= 4 Loo] [-9 (1 point) Find the least-squares solution x* of the system [ 1 | -1 ( 5 -2] [ 10 ] 2 X= 2 . 4 ] (-36]