GATE 2021 ST – Question 22

Matrix Theory · Vector Spaces and Linear Systems · 1 mark · Numerical answer

A has rows (0,0,1),(1,0,0),(0,1,0). Find the nullity of 5A(I₃+A+A²).

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Correct answer: 2 to 2

Explanation

A cycles the coordinates,and I+A+A² is the all-ones 3×3 matrix of rank one. Multiplying by nonzero scalar 5 and invertible A preserves that rank. Nullity=3−1=**2**.

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