Matrices & Determinants
Minors and cofactors
Grade Class 12
Question:
If Δ = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mtable><mtr><mtd><msub><mi>a</mi><mn>1</mn></msub></mtd><mtd><msub><mi>b</mi><mn>1</mn></msub></mtd><mtd><msub><mi>c</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><msub><mi>a</mi><mn>2</mn></msub></mtd><mtd><msub><mi>b</mi><mn>2</mn></msub></mtd><mtd><msub><mi>c</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><msub><mi>a</mi><mn>3</mn></msub></mtd><mtd><msub><mi>b</mi><mn>3</mn></msub></mtd><mtd><msub><mi>c</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced></math> and A2, B2, C2 are respectively cofactors of a2, b2, c2 then a1A2 + b1B2 + c1C2 is equal to -
(A) -Δ
(B) 0
(C) Δ
(D) none of these
Step-by-Step Solution
Key Concept: The sum of the product of elements of any row (or column) with the cofactors of a different row (or column) is always zero.
The sum of the product of elements of the first row (a1, b1, c1) with the cofactors of the second row (A2, B2, C2) is equal to 0. This is a standard property of determinants.
Correct Answer: 2