Project ForgeEngineering Mathematics
Linear Algebra
GATE 2014
Medium
Given that the determinant of the matrix [[1,3,0],[2,6,4],[−1,0,2]] is −12, the determinant of the matrix [[2,6,0],[4,12,8],[−2,0,4]] is
- −96
- B−24
- C24
- D96
Explanation
The second matrix is exactly the first matrix with every entry doubled (each row scaled by 2). Scaling every entry of an n×n matrix by a factor c scales the determinant by cⁿ. Here n=3 and c=2, so the new determinant = (−12)×2³ = (−12)×8 = −96.
Source: GATE ME 2014 (Session 1 / Set-1) (2014)
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