1. Consider the matrices and vectors given below: 3 1-3 0 4 1 2 A =...

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1. Consider the matrices and vectors given below: 3 1-3 0 4 1 2 A = 1 4 2, B=-4 0-2 u = 0 y= -3 -3 2 5 -1 2 0 3 1 b = -2 3 a. Show that AB BA b. Compute uTv and uvT. c. Calculate det (A). d. Compute (A+A)(B-BT). e. Find the inverse of A by using Gauss-Jordan elimination method [A |.I] [I | A] f. Find the inverse of A by computing its adjoint matrix. g. Find the inverse of B by computing its adjoint matrix. h. Find the solution for the matrix equation AX = b using Cramer's rule, where X is the vector of the unknowns (x1, x2, and x3) i. Find the solution for the matrix equation AX = b using A1, where X is the vector of the unknowns (x1, x2, and x3) 1. Consider the matrices and vectors given below: 3 1-3 0 4 1 2 A = 1 4 2, B=-4 0-2 u = 0 y= -3 -3 2 5 -1 2 0 3 1 b = -2 3 a. Show that AB BA b. Compute uTv and uvT. c. Calculate det (A). d. Compute (A+A)(B-BT). e. Find the inverse of A by using Gauss-Jordan elimination method [A |.I] [I | A] f. Find the inverse of A by computing its adjoint matrix. g. Find the inverse of B by computing its adjoint matrix. h. Find the solution for the matrix equation AX = b using Cramer's rule, where X is the vector of the unknowns (x1, x2, and x3) i. Find the solution for the matrix equation AX = b using A1, where X is the vector of the unknowns (x1, x2, and x3)