CBSE Class 12 Sample Paper for 2018 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

### If A = [a ij ] is a matrix of order 2 Γ 2, such that |A|Β  = β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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Question 2 (Method 1) If A = [πππ] is a matrix of order 2 Γ 2, such that |π΄| = β15 and Cππ represents the cofactor of πππ, then find π21 π21 + π22 π22 Given a is a 2 Γ 2 matrix A = [β 8(π_11&π[email protected]π_21&π_12 )] Given |A| = β 15 |A| = a11 a12 β a21 a12 β 15 = a11 a12 β a21 a12 a11 a12 β a21 a12 = β 15 Now, we need to find C21, C22 First we find minors M21 = |β 8(π_11&π[email protected]π_21&π_12 )| = a12 M22 = |β 8(π_11&π[email protected]π_21&π_12 )| = a11 C21 = (β1)2+1 M21 = β1 Γ a12 = β a12 C22 = (β1)2+2 M22 = 1 Γ a11 = a11 Now, π21 π21 + π22 π22 = π21 (βπ12 ) + π22 π11 = βπ21 π12 + π22 π11 = π22 π11 β π21 π12 = β 15 Question 2 (Method 2) If A = [πππ] is a matrix of order 2 Γ 2, such that |π΄| = β15 and Cππ represents the cofactor of πππ, then find π21 π21 + π22 π22 Determinant of a 2 Γ 2 matrix is given by |A| = π21 π21 + π22 π22 Given |A| = β 15 β 15 = π21 π21 + π22 π22 π21 π21 + π22 π22 = β 15