The official grading is **marks to all**. For every matrix, range(A³)⊆range(A²), so rank(A³)≤rank(A²). The printed strict inequality reverses this unavoidable monotonicity, and no matrix can satisfy the premises. The geometric multiplicity therefore cannot be inferred from a consistent example. The invalid premise is retained and explained.
More Eigenvalues and Canonical Forms questions
GATE 2021 MA Q62– V is the real vector space of polynomials p=a₀+a₁x+a₂x². Define…
GATE 2026 MA Q28– T reflects ℝ³ through a two-dimensional subspace. P is its matrix in the standard basis.…
GATE 2026 MA Q48– Nonzero real 3×3 matrices P,Q are simultaneously upper triangularizable by the same…
GATE 2026 MA Q55– Let J=pmatrix2&1&0&0&0&0\\0&2&0&0&0&0\\0&0&2&1&0&0\\0&0&0&2&0&0\\0&0&0&0&3&1\\0&0&0&0&0&3p…
GATE 2025 MA Q11– S is the set of unit vectors w∈ℝ³ for which A=(1,-3,2)TwT is diagonalizable. Which…
GATE 2025 MA Q23– For which invertible M is the difference of characteristic polynomials p M(x)−p (M⁻¹)(x)…