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Question

# If A=⎡⎢⎣012123234⎤⎥⎦ and B=⎡⎢⎣1−2−102−1⎤⎥⎦, then what would be third element in the second column of matrix AB?

A
-8
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B
-5
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C
5
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D
7
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Solution

## The correct option is A -8We know that two matrices can be multiplied only when number of columns of A = no. of rows of B. (for AB to be defined). In the above question the 2 matrices satisfy this condition. Also elements of AB are obtained by adding the products of corresponding elements of ith row of A and jth column of B. This will give (i,j)th element of AB. So ⎡⎢⎣012123234⎤⎥⎦⎡⎢⎣1−2−102−1⎤⎥⎦ =⎡⎢⎣(0×1)+(1×−1)+2×2(0×−2)+(1×0)+(2×−1)(1×1)+(2×−1)+3×2(1×−2)+(2×0)+(3×−1)(2×1)+(3×−1)+4×2(2×−2)+(3×0)+(4×−1)⎤⎥⎦ =⎡⎢⎣3−25−57−8⎤⎥⎦ So the third element of second column of this matrix will be -8 which is the correct answer.

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