Question

Lecture 11: question 2 • Which of the below is/are correct with respect to the product of two matrices? A The product AB is defined as the standard matrix of a composition of two linear transformations with the standard matrices A and B applied in the indicated order. B. The product AB is the matrix whose columns are the products of the matrix A and the columns of B. C. The entry (7) of AB is calculate as a sum of the products of the entries in row i of A and the corresponding entries in the column of B. D. The product AB is defined when the number of rows in A matches the number of columns in B. E Matrix multiplication is commutative: AB = BA. F. If AB = AC, then B = C.

Answer 1

incased c) false A is falle because it holds only fool - linear operates Gredem. Let T&t be linear operates on n-dimensional recaspace V(f). If By basis of v them [TH] =G] fie if A=[] 48= [ht] them [T H)= AB)) cave et par excemple A= 3) B-LED [614 6+16 7 lia 227 then AB= 15723 18482 = 43 goj © sec er See above example (1, 2) of AB is air element in AB Qiz = 4(6)+28) = 6716=22 metti sem of products of It low of A & and column of B

- ② incorrec (2) fabe If Amxn 4 Bmxp then only we define AB mxp le no. of soos colectons of A = no. of Doces MB © maved matwc multiplication is not Camutatul for example take above example en 1567 m 27.618 10.4267 +84 14+32 BA=178 L3 -res 347 Ls1 46 ABEBA incorect A 18 invertible then AB = 40 =) B=( fR does not mention Here A is invertible