Problem 9. (1 point) Let A be a 3 ! 2 matrix. Suppose we know that u = [2 \ -1] and v = [-1 \ -2] satisfy the equations Au = a and Av = b. Find a solution x to Ax = 4a + 5b. x = [ \ ] Problem 10. (1 point) Let A and B be symmetric n ! n matrices. For each of the following, determine whether the given matrix must be symmetric or could be non symmetric. ? 1. H = AB - BA ? 2. F = ABA ? 3. G = AB + BA ? 4. E = AB ? 5. C = A + B ? 6. D = A^2 Problem 11. (1 point) Find the inverse of AB if A^-1 = [-1 2 \ 3 -3] and B^-1 = [4 -4 \ 5 -3] (AB)^-1 = [ ]
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We can write the equation as: Ax = 4(Au) + 5(Av) Since A is a 3x2 matrix, we can write it as: A = [a1 a2] [a3 a4] [a5 a6] where a1, a2, a3, a4, a5, a6 are the entries of A. Then, we can write the equation as: [x1 x2] [a1 a2] = 4[u1 u2] + 5[v1 v2] Show more…
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Problem 9. (1 point) Let A be a 3 x 2 matrix. Suppose we know that u and v satisfy the equations Au = a and Av = b. Find a solution x to Ax = 4a + 5b. Problem 10. (1 point) Let A and B be symmetric n x n matrices. For each of the following, determine whether the given matrix must be symmetric or could be non-symmetric. 1. H = AB - BA 2. F = ABA 3. G = AB + BA 4. E = AB 5. C = A + B 6. D = A^2 Problem 11. (1 point) Find the inverse of AB if
Adi S.
Question 3 (a) Given the matrices, P = [3 -2; 7 -4], Q = [-4 2; -7 3], find (i) PQ (ii) QP (iii) Write a possible relationship between P and Q. (b) (i) Find a and b if 4[a 2; -1 3a] + [b -2; 5 -b] = [7 6; 1 1] (ii) If A = [3 2; -1 1] and B = [0 -4; -2 8], find matrices X such that 2A + X = B (c) Given A = [0 1; 2 3]. (i) Show that A is non-singular. (ii) Find B such that BA^2 = A (d) The matrix A = [3 -5; -1 2] is the inverse of B = [2 5; 1 3]. Verify this statement. [Hint: You need to show that AB = BA = I]
Sri K.
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