Ans. 5.
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5. Let A-L 7 B = 3 A = 5k What values of k, if any, will make AB = BA?
Find AB and BA, if possible. (If not possible, enter IMPOSSIBLE in any single blank.) 5 -4 -5 31 B = 1 3 5 - AB = 11 BA = 11 Find AB and BA, if possible. (If not possible, enter IMPOSSIBLE in any single blank. A = 0 4 1 -3 1 -3 3 0 AB= 1 ВА =
44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove that det ((-A-t +1 where t = Tr(A).
44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove...
(3) Let A = 2 5 3 8 and B = –7 4 -95 Compute the matrix products AB and BA.
4. Let A and B be n x n such that B = 1-A and A2 = A. Show that AB BA = 0 4. Let A and B be n x n such that B 1-A and A2 = A. Show that AB-BA-0
4. Let A and B be n x n such that B = 1-A and A2 = A. Show that AB BA = 0
4. Let A and B be n x n such that B...
1. Let a and b be elements of a group
. Prove that ab and ba have the same order.
2. Show by example that the product of elements of nite order in a
group need not
have nite order. What if the group is abelian?
P.2.16 Let V= span {AB-BA : A, B E Mn. (a) Show that the function tr : M,,-> C is a linear transformation. (b) Use the dimension theorem to prove that dim ker tr = n2-1. (c) Prove that dim V = n2-1. (d) Let Eij=eie), every entry of which is zero except for a 1 in the (i, j) position. Show that k,-OikEil for l i, j, k, n. (e) Find a basis for V. Hint: Work out the...
-3 3 25 A= 5 7 and B= 4. 1 (a) Find AB if possible. (b) Find BA if possible. (c) Find A’ if possible. (Hint: A² = A : A.)
Problem 6 Let A, B, C Rnxn where AB = BA = In and AC = CA = Γη. Show that B-C
-4 2 5 5 -5 Find (if possible) a. AB and b. BA, if A = 2 - 5 B = 4 4 - 2 0 3 a. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. AB = (Simplify your answers.) OB. This matrix operation is not possible. b. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. BA=...
suppose a firm has a cobb-douglas weekly production function q=f(l,k)=25l^.5k^.5, where l is the number of workers and k is units of capital.mrtslk is k/l. the wage rate is $900 per week, and a unit of capital costs $400 per week. what is the least cost input combination for producing 675 units of output?