Matrices and Determinants 4 Question 17

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18. The number of 3×3 matrices A whose entries are either x1 0 or 1 and for which the system Ay=0 has exactly z 0

======= ####18. The number of 3×3 matrices A whose entries are either 0 or 1 and for which the system A[xyz] =[100] has exactly

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed two distinct solutions, is

(2010)

(a) 0

(b) 291

(c) 168

(d) 2

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Answer:

Correct Answer: 18. (a)

Solution:

  1. Since, A[xyz] =[100] is linear equation in three variables and that could have only unique, no solution or infinitely many solution.

It is not possible to have two solutions.

Hence, number of matrices A is zero.



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