Matrices & Determinants
Counting singular matrices
nta_pyq_2025_apr
Grade 12
Question:
The number of singular matrices of order 2 , whose elements are from the set {2, 3, 6, 9} is
Step-by-Step Solution
Key Concept: Apply the matrix property for counting singular matrices and reduce it to determinant or parameter equations.
|a | d| | =$ad - bc$$\Rightarrow$$ad = bc$(36) | b c |$Case-I$Exactly 1 no. is used 4 $\Rightarrow$ All singular =$C_{1}$$Case-II$Exactly 2 no. is used 4 $\Rightarrow$$C_{2}$$\times$ 2 $\times$ 2$Case-III$Exactly 3 no. is used None will be singular$Case-IV$Exactly 4 No. is used$ad=bc$$\Rightarrow$ 2 $\times$$9 = 3$$\times$ 6 |9 -| 4 | | $\Rightarrow$$C_{1}$$\times$ 21 |- 2 |$Total = 36$
Correct Answer: 36