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If a matrix A is _______ and the product AB is _______, what is the size of matrix B?

1 Answer

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Final answer:

The missing words in the question are likely 'invertible' and 'defined'. The size of matrix B is determined by the dimensions of matrix A.

Step-by-step explanation:

The question is missing some essential information, but based on the available details, we can deduce that the missing word in the first blank is 'invertible' or 'non-singular', indicating that the matrix A has an inverse or is non-singular. The missing word in the second blank could be 'defined', 'valid', or 'computable', indicating that the product AB is defined or valid.



Given that A is invertible and AB is defined, the size or dimensions of matrix B can be determined by examining the compatibility condition for matrix multiplication. The number of columns in A must be equal to the number of rows in B. So if matrix A is m x n, then matrix B must be n x p, where 'n' represents the number of columns in matrix A and 'p' represents the number of columns in matrix B.

User Yusuke Kawabata
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