Which of the following statements are true and which are false? Give r

Question

Which of the following statements are true and which are false? Give reasons for your answer

i) If $V$ is a finite dimensional vector space and $T:V \to V$ is a diagonalisable linear operator, then there is a basis, unique up to order of the elements, with respect to which the matrix of $T$
is diagonal.
ii) Up to similarity, there is a unique $3 \times 3$ matrix with minimal polynomial $(x-1)^2(x-2)$ .
iii) If $\lambda$ is the eigenvalue of a matrix

06 Feb 2024

Answer :

Word Count : 263

Let's analyze each statement:

i) If $ V $ is a finite-dimensional vector space and $ T:V \rightarrow V $ is a diagonalizable linear operator, then there is a basis, unique up to the order of the elements, with respect to which the ___ _________ _________ _________ __________ ___ _______ ____ _________ ___ _____ ______.
____ ______ ___ ______ ____ _________ _____ ________.
________ ________ __________ ________ ______ _____ _________ ________ _______ ________ _____ ______.
__________ ________ _________ _______ _________ ____ _________ ____.
___ ___ _______ __________ ______ _____.
________ _____ _____ ________ _____.
_________ _____ ____ _____ _________ _________ __________ _______ _________ ____ ______.
________ ______ ______ ______ __________ ____ _______ ________ _________.
____ ___ _____ _____ _________ _______ _______ ____ __________.
_____ ________ ______ __________ _____ _____ _____ _______.
_________ ____ _________ _______ ____ ______ _________ _____ ________ ___.
____ ___ ________ __________ ___.
____ _______ ____ ______ ___ ________ _______ _______ ________ ____ ________ ________.
__________ _________ _________ _______ ________.
______ ____ __________ _________ ___ _______ __________ _____.
____ ________ ___ ______ _____ __________.
__________ _____ _________ ______ _______ ________ ________ _____ ____.
_____ ________ ________ ____ ___ _______ _______.
__________ _________ ______ ______ _______ _________ __________ ____ _________.
______ ___ ________ _____ ____.
________ _______ _______ __________ ______ __________ ___ ____ ____ _____.
_______ ___ ________ ____ ________ ____ _________.
______ ____ ____ _________ ______ _____ ____ ____ ____ _________ _____ _______.
_______ _________ _________ ________ ________ ___ ____ ____ _________ _______ _______.
__________ ___ _____ _________ _____.
_________ _____ _____ ______ ________ _________ ____ _________ ______ ________ ____.
Get Full Answer on WhatsApp

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers

IGNOU NEWS

Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★