GATE 2026 MA – Question 28
Linear Algebra · Eigenvalues and Canonical Forms · 1 mark · Numerical answer
T reflects ℝ³ through a two-dimensional subspace. P is its matrix in the standard basis. Find 2 trace(P) − 3 det(P) (integer).
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Correct answer: 5 to 5
Explanation
Reflection fixes the plane (two eigenvalues +1) and reverses its normal (one eigenvalue −1). Trace = 1+1−1 = 1; determinant = −1. Required value = 2×1−3(−1) = **5**.
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