Question 2 - CBSE Class 12 Sample Paper for 2018 Boards
Last updated at Nov. 30, 2018 by Teachoo

Subscribe to our Youtube Channel - https://www.youtube.com/channel/UCZBx269Tl5Os5NHlSbVX4Kg

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

You can download the question paper here
https://www.teachoo.com/cbse/sample-papers/

Transcript

Question 2 (Method 1)
If A = [๐๐๐] is a matrix of order 2 ร 2, such that |๐ด| = โ15 and C๐๐ represents the cofactor of ๐๐๐, then find ๐21 ๐21 + ๐22 ๐22
Given a is a 2 ร 2 matrix
A = [โ 8(๐_11&๐_12@๐_21&๐_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_11&๐_12@๐_21&๐_12 )| = a12
M22 = |โ 8(๐_11&๐_12@๐_21&๐_12 )| = a11
C21 = (โ1)2+1 M21 = โ1 ร a12 = โ a12
C22 = (โ1)2+2 M22 = 1 ร a11 = a11
Now,
๐21 ๐21 + ๐22 ๐22 = ๐21 (โ๐12 ) + ๐22 ๐11
= โ๐21 ๐12 + ๐22 ๐11
= ๐22 ๐11 โ ๐21 ๐12
= โ 15
Question 2 (Method 2)
If A = [๐๐๐] is a matrix of order 2 ร 2, such that |๐ด| = โ15 and C๐๐ represents the cofactor of ๐๐๐, then find ๐21 ๐21 + ๐22 ๐22
Determinant of a 2 ร 2 matrix is given by
|A| = ๐21 ๐21 + ๐22 ๐22
Given |A| = โ 15
โ 15 = ๐21 ๐21 + ๐22 ๐22
๐21 ๐21 + ๐22 ๐22 = โ 15

Show More