DeterminantHard
Question
Let A = 
where a,b, c, d, e ∈ {0, 1}
then number of such matrix A for which system of equation AX = 0 have unique solution.
where a,b, c, d, e ∈ {0, 1}then number of such matrix A for which system of equation AX = 0 have unique solution.
Options
A.16
B.6
C.5
D.none
Solution
|A| ≠ 0
a(ed - 0) + b (0 - ce)
|A| = aed - bce = e (ad - bc) ≠ 0
e = 1 and ad - bc ≠ 0
ad - bc = 1 if [ad = 1, bc = 0] Total = 3
ad - bc = -1 if [ad = 0, bc = 1] Total = 3
Total = 3 + 3 = 6
a(ed - 0) + b (0 - ce)
|A| = aed - bce = e (ad - bc) ≠ 0
e = 1 and ad - bc ≠ 0
ad - bc = 1 if [ad = 1, bc = 0] Total = 3
ad - bc = -1 if [ad = 0, bc = 1] Total = 3
Total = 3 + 3 = 6
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