For 𝑛 1, the maximum multiplicity of any eigenvalue of an 𝑛×𝑛 matrix with elements from ℝ is

Question

For 𝑛 > 1, the maximum multiplicity of any eigenvalue of an 𝑛×𝑛 matrix with elements from ℝ is

Accepted Answer

Correct answer: A — The multiplicity of an eigenvalue refers to its algebraic multiplicity, i.e., the number of times it appears as a root of the characteristic polynomial. For an n×n matrix: The characteristic polynomial has degree n. Therefore, the sum of the algebraic multiplicities of all eigenvalues is exactly n. Hence, the maximum possible multiplicity of a single eigenvalue is n.

Answer

A. n

Answer

B. n-1

Answer

C. 1

Answer

D. n+1

For 𝑛 > 1, the maximum multiplicity of any eigenvalue of an 𝑛×𝑛 matrix with…