   Chapter 1.6, Problem 4E

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# Let A =   [ a i j ] 2     ×     3 where a i j = i + j , and let B = [ b i j ] 3     ×     4 where b i j = 2 i − j . If A B = [ c i j ] 2     ×     4 , write a formula for c i j in terms of i   and j .

To determine

A formula for cij in terms of i and j for A=[aij]2×3 where aij=i+j,

B=[bij]3×4 where bij=2ij and AB=[cij]2×4.

Explanation

Given information:

A=[aij]2×3 where aij=i+j,

B=[bij]3×4 where bij=2ij and AB=[cij]2×4.

Formula used:

Definition: Matrix multiplication

The product of m×n matrix A over and n×p matrix B over is m×p matrix C=AB, where the element cij in row i and column j of AB is found by using the elements in row i of A, and the elements in column j of B in the following manner:

columnjofBcolumnjofCrowiofA[ai1ai2ai3ain][b1

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