Question

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1) Let A, B, C, and D be the matrices defined below. Compute the matrix expressions when they are defined; if an expression is undefined, explain why. [2 0-1] [7 -5 A= .B -5 -4 1 C- ,D= (-5 3] [I -3 a) AB b) CD c) DB d) 3C-D e) A+ 2B 2) Let A and B be the matrices defined below. 4 -2 3) A=-3 0, B= 3 5 a) Compute AB using the definition of matrix multiplication b) Compute AB using the "Row-Column Rule" for matrix multiplication. I

Answer 1

© A = 20 -5 1 14 -5 2 and D= [-5 3 @ AB is undefined as A is a 2x3 matrix and B is a 2x3 matrix. so, the number of columns of matrix A is not equal to the number of rows of matrix B & hence AB is not defined. ② CD is also undefined. C is a 2x2 matrix & D is a 1x2 matrix. so, the number of columns of c is not equals to the number of rows of Dand hence CD is not defined. © DB is defined as D is a 1x2 matrixf Bis a 2x3 matrix & hence DB is a 1×3 matrix. .: DB = [-5 37 57 - 5 1 -4 -3 5132 13 -14 [-32 13 -34] (3c-D) is undefined. We know that difference of two matrix possible if both matrix are of same order. Here is a 2x2 matix & D is a 1x2 matrix, which are not same. so,(3c-0) is not defined. © (A+2B) is defined. (A+2B) = [.5 -1]+2 [1 =4 -3 3) 3 ] - + 2 0 2 6 -10 1 4 - 0 2 2 -8 -6 4 -5 13:47