Question

Let \( A = (a_{ij}) \) be a square matrix of order 3 and let \( M_{ij} \) be the minors of \( a_{ij} \). If \( M_{11} = -40, M_{12} = -10, M_{13} = 35 \), and \( a_{11} = 1, a_{12} = 3, a_{13} = -2 \), then the value of \( |A| \) is equal to:

• A. -100
• B. -80
• C. 0
• D. 60
• E. 80

Hint:

Use cofactor expansion to calculate the determinant of a 3x3 matrix. Remember that the sign alternates with each cofactor.

Answer 1

The Correct Option is B

The determinant of the matrix \( A \), denoted \( |A| \), can be calculated using the cofactor expansion. 
The formula is: \[ |A| = a_{11} M_{11} - a_{12} M_{12} + a_{13} M_{13} \] Substituting the given values: \[ |A| = (1)(-40) - (3)(-10) + (-2)(35) = -40 + 30 - 70 = -80 \]