Q. 215.0( 1 Vote )

Given an example

Answer :

We need to form matrices A, B and C such that AB = AC, where A is a non-zero matrix, but B ≠ C.

Take,





First, compute AB.



Multiply 1st row of matrix A by matching members of 1st column of matrix B, then sum them up.


(1, 0)(1, 2) = (1 × 1) + (0 × 2)


(1, 0)(1, 2) = 1 + 0


(1, 0)(1, 2) = 1



Similarly, let us do the same for other elements.





Now, let us compute AC.



Multiply 1st row of matrix A by matching members of 1st column of matrix C, then sum them up.


(1, 0)(1, 2) = (1 × 1) + (0 × 2)


(1, 0)(1, 2) = 1 + 0


(1, 0)(1, 2) = 1



Similarly, let us do the same for other elements.





Clearly, AB = AC.


Thus, we have found an example that satisfy the required criteria.


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