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

This is a question of CBSE Sample Paper - Class 12 - 2017/18.

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If A = [aij] is a matrix of order 2 x 2, |A| = -15 and Cij is cofactor

Question 2 - CBSE Class 12 Sample Paper for 2018 Boards - Part 2
Question 2 - CBSE Class 12 Sample Paper for 2018 Boards - Part 3

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Transcript

Question 2 (Method 1) If A = [π‘Žπ‘–π‘—] is a matrix of order 2 Γ— 2, such that |𝐴| = βˆ’15 and C𝑖𝑗 represents the cofactor of π‘Žπ‘–π‘—, then find π‘Ž21 𝑐21 + π‘Ž22 𝑐22 Given a is a 2 Γ— 2 matrix A = [β– 8(π‘Ž_11&π‘Ž_12@π‘Ž_21&π‘Ž_12 )] Given |A| = – 15 |A| = a11 a12 – a21 a12 – 15 = a11 a12 – a21 a12 a11 a12 – a21 a12 = – 15 Now, we need to find C21, C22 First we find minors M21 = |β– 8(π‘Ž_11&π‘Ž_12@π‘Ž_21&π‘Ž_12 )| = a12 M22 = |β– 8(π‘Ž_11&π‘Ž_12@π‘Ž_21&π‘Ž_12 )| = a11 C21 = (–1)2+1 M21 = –1 Γ— a12 = – a12 C22 = (–1)2+2 M22 = 1 Γ— a11 = a11 Now, π‘Ž21 𝑐21 + π‘Ž22 𝑐22 = π‘Ž21 (βˆ’π‘Ž12 ) + π‘Ž22 π‘Ž11 = βˆ’π‘Ž21 π‘Ž12 + π‘Ž22 π‘Ž11 = π‘Ž22 π‘Ž11 βˆ’ π‘Ž21 π‘Ž12 = – 15 Question 2 (Method 2) If A = [π‘Žπ‘–π‘—] is a matrix of order 2 Γ— 2, such that |𝐴| = βˆ’15 and C𝑖𝑗 represents the cofactor of π‘Žπ‘–π‘—, then find π‘Ž21 𝑐21 + π‘Ž22 𝑐22 Determinant of a 2 Γ— 2 matrix is given by |A| = π‘Ž21 𝑐21 + π‘Ž22 𝑐22 Given |A| = – 15 – 15 = π‘Ž21 𝑐21 + π‘Ž22 𝑐22 π‘Ž21 𝑐21 + π‘Ž22 𝑐22 = – 15

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.