Question 2 (Method 1)
If A = [πππ] is a matrix of order 2 Γ 2, such that |π΄| = β15 and Cππ represents the cofactor of πππ, then find π21 π21 + π22 π22
Given a is a 2 Γ 2 matrix
A = [β 8(π_11&π_12@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_12@π_21&π_12 )| = a12
M22 = |β 8(π_11&π_12@π_21&π_12 )| = a11
C21 = (β1)2+1 M21 = β1 Γ a12 = β a12
C22 = (β1)2+2 M22 = 1 Γ a11 = a11
Now,
π21 π21 + π22 π22 = π21 (βπ12 ) + π22 π11
= βπ21 π12 + π22 π11
= π22 π11 β π21 π12
= β 15
Question 2 (Method 2)
If A = [πππ] is a matrix of order 2 Γ 2, such that |π΄| = β15 and Cππ represents the cofactor of πππ, then find π21 π21 + π22 π22
Determinant of a 2 Γ 2 matrix is given by
|A| = π21 π21 + π22 π22
Given |A| = β 15
β 15 = π21 π21 + π22 π22
π21 π21 + π22 π22 = β 15
Made by
Davneet Singh
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.
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