If A = [a ij ] is a matrix of order 2 × 2, such that |A|  = −15  and C ij represents the cofactor of a ij , then find a 21 c 21 + a 22 c 22

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Question 2 (Method 1) If A = [๐‘Ž๐‘–๐‘—] is a matrix of order 2 ร— 2, such that |๐ด| = โˆ’15 and C๐‘–๐‘— represents the cofactor of ๐‘Ž๐‘–๐‘—, then find ๐‘Ž21 ๐‘21 + ๐‘Ž22 ๐‘22 Given a is a 2 ร— 2 matrix A = [โ– 8(๐‘Ž_11&๐‘Ž_12@๐‘Ž_21&๐‘Ž_12 )] Given |A| = โ€“ 15 |A| = a11 a12 โ€“ a21 a12 โ€“ 15 = a11 a12 โ€“ a21 a12 a11 a12 โ€“ a21 a12 = โ€“ 15 Now, we need to find C21, C22 First we find minors M21 = |โ– 8(๐‘Ž_11&๐‘Ž_12@๐‘Ž_21&๐‘Ž_12 )| = a12 M22 = |โ– 8(๐‘Ž_11&๐‘Ž_12@๐‘Ž_21&๐‘Ž_12 )| = a11 C21 = (โ€“1)2+1 M21 = โ€“1 ร— a12 = โ€“ a12 C22 = (โ€“1)2+2 M22 = 1 ร— a11 = a11 Now, ๐‘Ž21 ๐‘21 + ๐‘Ž22 ๐‘22 = ๐‘Ž21 (โˆ’๐‘Ž12 ) + ๐‘Ž22 ๐‘Ž11 = โˆ’๐‘Ž21 ๐‘Ž12 + ๐‘Ž22 ๐‘Ž11 = ๐‘Ž22 ๐‘Ž11 โˆ’ ๐‘Ž21 ๐‘Ž12 = โ€“ 15 Question 2 (Method 2) If A = [๐‘Ž๐‘–๐‘—] is a matrix of order 2 ร— 2, such that |๐ด| = โˆ’15 and C๐‘–๐‘— represents the cofactor of ๐‘Ž๐‘–๐‘—, then find ๐‘Ž21 ๐‘21 + ๐‘Ž22 ๐‘22 Determinant of a 2 ร— 2 matrix is given by |A| = ๐‘Ž21 ๐‘21 + ๐‘Ž22 ๐‘22 Given |A| = โ€“ 15 โ€“ 15 = ๐‘Ž21 ๐‘21 + ๐‘Ž22 ๐‘22 ๐‘Ž21 ๐‘21 + ๐‘Ž22 ๐‘22 = โ€“ 15

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.