The GATE Grind

GATE 2020 BM – Question 27

Engineering Mathematics · Linear Algebra · 1 mark · Numerical answer

A nonsingular 3×3 matrix P has eigenvalues 1,2,3. Find trace(P⁻¹), to two decimals.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 1.82 to 1.84

Explanation

The inverse has eigenvalues 1,1/2,1/3. The trace equals their sum, including algebraic multiplicities, even without assuming diagonalizability. Thus trace=1+.5+.333333=11/6=1.833333, rounded to 1.83.

More Linear Algebra questions

All Linear Algebra questions →