Bonus Question for undergraduates (20 points). Mandatory for grad- uate students what is the determinant of...
Verify the following properties, using any distinct, invertible A, B, 4×4 upper triangular matrices of your choice: 3. (0.5 marks each) Verify the following properties, using any distinct, invertible A, B, 4 x 4 upper triangular matrices of your choice: (a) The inverse of an upper triangular matrix is upper triangular; (b) (AB)- B-1A-1 (e) trace(AB) trace(BA); (d) det(AB) det (BA) example of matrices A, B such that det(AB) det(BA) (BONUS 1 mark) Give an 3. (0.5 marks each) Verify...
HW10P5 (10 points) 3 2 -1 Let A be the matrix A = 1-3 0 6 -2 1 a. (4 pts) Find the multipliers l21, 131,132 and the elemention matrices E21, E31, E32 b. (2 pts) Use the multipliers l21, 131,132 to construct the lower triangular matrix, L c. (2 pts) Use the elimination matrices to determine the upper triangular, U, matrix of A d. (2 pts) verify that LU A
1 2 2 1 -X Find the determinant of the matrix as a formula in terms of x and y. Remember to use the correct syntax for a formula 0 0 1 -3 -x X Question 4: (2 points) a b c fis 3, find the determinant of these matrices: If the determinant of the matrix M = d e (gh k) b a C (a) 7 d 7e 7f h k -E. b-2 e c - 2 f a...
HW10P5 (10 points) Let A be the matrix A =13 5 0 (3 pts) Find the elementary matrices that perform the following row operations in sequence: a. 21 * 2 2. E31 : R3 R1R3 b. (3 pts) Show that the elementary matrices you found in (a) can be used as elimination matrices to determine the upper triangular, U, matrix of A. (4 pts) Find the lower triangular, L, matrix that verifies A C. = LU.
linear algebra Let V (71, 72, 3}, where 71 73=(2,0,3). (1,3,-1), 2 = (0, 1,4), and (a) Prove: V is a basis. (b) Find the coordinates of (b, b2, bs) with respect to V = {71, U2, 3,}. (c) Suppose M and M' are matrices whose columns span the same vector space V. Let b be the coordinates of relative to M. Write a matrix equation that gives b', the coordinates of relative to M'. (Your answer should be a...
Bonus Points: For 20 Bonus Points, construct two flow charts as to how you would test an unknown solution that might contain any of the following ions. Cations: Na, K+, Li+, Ca+2, Ba+2, Sr+, Cu+2, Al+3, Fe+2, Fe+3, Zn+2, NH4+ Anions: Cl-, Br, l, CO3-2. CIO-, SO3-2, S04-2, PO4-3
Bonus Points: For 20 Bonus Points, construct two flow charts as to how you would test an unknown solution that might contain any of the following ions. Cations: Na, K+, Li+, Ca+2, Ba+2, Sr+, Cu+2, Al+3, Fe+2, Fe+3, Zn+2, NH4+ Anions: Cl-, Br, l, CO3-2. CIO-, SO3-2, S04-2, PO4-3
Question 19 [10 points] If the determinant of the first matrix below is as given, find the determinant of the other matrix. a b c det r s t 5 x y z 2x 2y 2z a+2x b+2y c+2z Official Time: 22:24:28 SUBMIT AND MARK
1. (All students!) For matrices with special properties, it is possible to create special versions of Gauss elimination. Suppose matrix A (nxn) is symmetric (which means that A-A). Suppose also that A is positive definite; this means that the scalar = xTAx is always 20 for every vector x , and J-0 only if x = 0 In this case it can be shown that the usual Gauss elimination process, which effectively creates the factorization A LU, can be simplified...
PLEASE, ANSWER ALL SUBPARTS AND ALL THE EXERCISES!! DO NOT DO JUST ONE. ALSO, SHOW COMPLETE STEPS. THANK YOU! 1. Find the determinant of each of the matrices below using (1) row operations-transforming each matrix to an upper-triangular form or (2) cofactor expansion. (a) A = ſi 1 1 1 2 2 2 3 (b) A= ſi 2 3 2 2 3 0 3 0 1 (c) A [1 0 0 1 0 1 1 1 0 1 1 0...