Enter T or F depending on whether the statement is true or false. (You must ente
ID: 3142789 • Letter: E
Question
Enter T or F depending on whether the statement is true or false. (You must enter T or F True and False will not work.) If AB is defined, then BA is also defined. If A has dimensions 5 times 4 and B has dimensions 4 times 3, then the 3rd row, 2nd column entry of AB is obtained by multiplying the 2nd column of A by the 3rd row of B. If A has dimensions m times n and B has dimensions n times r, then AB has dimensions m times r. If A has dimensions m times r and B has dimensions r times n, then AB has dimensions r times n.Explanation / Answer
1. AB is defined, then BA is also defined - F.
Reason: AB is defined implies number of columns in A = Number of rows in B. However the number of rows in A need not be equal to the number of columns in B. So BA need not be defined.
2. The 3rd row, 2nd column entry of AB is obtained by multiplying the 3rd row of A and 2nd column of B.
So the answer is F.
3. If A has dimensions m x n and B has dimensions n x r, then AB has dimensions m x r. The statement is T.
4. If A has dimensions m x r and B has dimensions r x n, then AB has dimensions m x n. The statement is F.
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