The number of 3 3 matrices A whose entries are either 0 or 1 and for which the system A bmatrix x bmatrix = bmatrix 1 0 0 bmatrix has exactly two distinct solutions, is

JEE Advanced 2010 Mathematics question

The number of matrices A whose entries are either 0 or 1 and for which the system has exactly two distinct solutions, is

(A)Correct
(B)
(C)
(D)

Answer: (A)

Solution

A system of linear equations over the real numbers has either no solution, exactly one solution, or infinitely many solutions. Indeed, if are two distinct solutions, then for every real , , so

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Question ID VK-025766