Given that A = [𝑎𝑖𝑗] is a square matrix of order 3 × 3 and |A| = −7, then the value of ∑_(i=1) 3 a i2 A i2 " , where 𝐴 𝑖𝑗 denotes the cofactor of element 𝑎𝑖𝑗 is:
(a) 7 (b) −7 (c) 0 (d) 49
CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
Last updated at Dec. 16, 2024 by Teachoo
Transcript
Question 17 Given that A = [𝑎𝑖𝑗] is a square matrix of order 3 × 3 and |A| = −7, then the value of ∑_(𝑖=1)^3▒"𝑎𝑖2𝐴𝑖2 " , where 𝐴𝑖𝑗 denotes the cofactor of element 𝑎𝑖𝑗 is: (a) 7 (b) −7 (c) 0 (d) 49 Now, = 𝒂_𝟏𝟐 𝑨_𝟏𝟐+𝒂_𝟐𝟐 𝑨_𝟐𝟐+𝒂_𝟐𝟐 𝑨_𝟏𝟐 = Sum of product of elements of Row R2 with its corresponding cofactors = Determinant of A = |A| = 7 So, the correct answer is (B)