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Solution


Q.

The number of singular matrices of order 2, whose elements are from the set {2, 3, 6, 9}, is __________.          [2025]

Ans.

(36)

For any singular matrix [acbd]; we have

|acbd|=ad–bc=0 ⇒ ad=bc

Case I : Exactly one number is used

                ⇒  All like, then required number = C14 = 4

Case II : Exactly two number i.e., (a, a, a, b or a, a, b, b) are used, then required number

                ⇒ C24×2×2=24

Case III : Exactly three numbers i.e., (a, a, b, c) are used, then none will be singular.

Case IV : Exactly four number i.e., (a, b, c, d) are used, then ad = bc i.e.,

                2×9=3×6 ⇒ C14×2!=8 

Total number of matrices = 36.