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Determinant of a 2×2 matrix [[a,b],[c,d]] equals
Aad − bc
Bab + cd
Ca + d
Da × d × b × c
Answer & Solution
Correct answer: A. ad − bc
1. Determinant of [[a,b],[c,d]] = a·d − b·c.
2. Geometrically equals the signed area of the parallelogram spanned by the rows.
3. Equal to zero ⇔ the rows are linearly dependent (matrix not invertible).
4. Hence (B) is correct.
_Source: Maharashtra Balbharati Std XII Mathematics & Statistics (Commerce), Ch 1 "Matrices", §1.3 ¶§1.3_
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