Given that A = [๐‘Ž๐‘–๐‘—] is a square matrix of order 3 × 3 and |A| = −7, then the value of ∑_(i=1) 3 a i2 A i2 "  , where ๐ด ๐‘–๐‘— denotes the cofactor of element ๐‘Ž๐‘–๐‘—  is:

(a) 7  (b) −7  (c) 0  (d) 49

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  1. Class 12
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Transcript

Question 17 Given that A = [๐‘Ž๐‘–๐‘—] is a square matrix of order 3 ร— 3 and |A| = โˆ’7, then the value of โˆ‘_(๐‘–=1)^3โ–’"๐‘Ž๐‘–2๐ด๐‘–2 " , where ๐ด๐‘–๐‘— denotes the cofactor of element ๐‘Ž๐‘–๐‘— is: (a) 7 (b) โˆ’7 (c) 0 (d) 49 Now, = ๐’‚_๐Ÿ๐Ÿ ๐‘จ_๐Ÿ๐Ÿ+๐’‚_๐Ÿ๐Ÿ ๐‘จ_๐Ÿ๐Ÿ+๐’‚_๐Ÿ๐Ÿ ๐‘จ_๐Ÿ๐Ÿ = Sum of product of elements of Row R2 with its corresponding cofactors = Determinant of A = |A| = 7 So, the correct answer is (B)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.