Let P =Thena)P has two linearly independent eigenvectorsb)P has an eigen vectorc)P is non singulard)There exists a non singular matrix S such that S-1PS is a diagonal matrix.Correct answer is option 'B'. Can you explain this answer?

EduRev

All Courses

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

Mathematics Exam > Mathematics Questions > Let P =Thena)P has two linearly independent e...

Join the Discussion on the App

Let P =

Then

a)
P has two linearly independent eigenvectors
b)
P has an eigen vector
c)
P is non singular
d)
There exists a non singular matrix S such that S^-1PS is a diagonal matrix.

Correct answer is option 'B'. Can you explain this answer?

FREE This question is part of

Matrix MCQ - 4

Attempt Test

Attempt this Test

Verified Answer

Let P =Thena)P has two linearly independent eigenvectorsb)P has an eig...

eigenvalues are given by |P — λI| = 0
λ = 0,0 not distinct
=>P is not diagonalizable

=> singular (also, |P| = 0, product of eigenvalues)
eigenvector corresponding to λ = 0 is given by

X₁ + ix₂ = 0 after apply R₂ → R₂ — iR₁
P has only one eigenvector
P is diagonalizable if algebraic multiplicity and geometric multiplicity of eigenvalues are equal. λ = 0 has algebraic multiplicity 2 whereas its geometric multiplicity is 1.
Hence, P is not diagonalisable.

View all questions of this test

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for Mathematics exam

Similar Mathematics Doubts

Square matrix A of order n over R has rank n. Which one of the following statement is not correct?

View answer

Let T : V --> U be a linear transformation such that T maps independent sets into independent sets, then

View answer

Let X and Y are n x n matrices with real entries, then which of the following is(ar e) true?

View answer

Let T : R3 --> R3 be defined by T(x, y, z) = (x, y, 0) and S : R2 —> R2 be defined by S(x, y) =(2x, 3y), be linear transformations on the real vector spaces R3 and R2, respectively. Then, which one of the following statement is correct?

View answer

Let T:V-V be the linear transformation such as Tf(t)=tft), where f(t) is a polynomial. Then, Tis singular Tis non-singular T is onto None of these?

View answer

Let P =Thena)P has two linearly independent eigenvectorsb)P has an eigen vectorc)P is non singulard)There exists a non singular matrix S such that S-1PS is a diagonal matrix.Correct answer is option 'B'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
Let P =Thena)P has two linearly independent eigenvectorsb)P has an eigen vectorc)P is non singulard)There exists a non singular matrix S such that S-1PS is a diagonal matrix.Correct answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let P =Thena)P has two linearly independent eigenvectorsb)P has an eigen vectorc)P is non singulard)There exists a non singular matrix S such that S-1PS is a diagonal matrix.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let P =Thena)P has two linearly independent eigenvectorsb)P has an eigen vectorc)P is non singulard)There exists a non singular matrix S such that S-1PS is a diagonal matrix.Correct answer is option 'B'. Can you explain this answer?.

Solutions for Let P =Thena)P has two linearly independent eigenvectorsb)P has an eigen vectorc)P is non singulard)There exists a non singular matrix S such that S-1PS is a diagonal matrix.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.

Here you can find the meaning of Let P =Thena)P has two linearly independent eigenvectorsb)P has an eigen vectorc)P is non singulard)There exists a non singular matrix S such that S-1PS is a diagonal matrix.Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let P =Thena)P has two linearly independent eigenvectorsb)P has an eigen vectorc)P is non singulard)There exists a non singular matrix S such that S-1PS is a diagonal matrix.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Let P =Thena)P has two linearly independent eigenvectorsb)P has an eigen vectorc)P is non singulard)There exists a non singular matrix S such that S-1PS is a diagonal matrix.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Let P =Thena)P has two linearly independent eigenvectorsb)P has an eigen vectorc)P is non singulard)There exists a non singular matrix S such that S-1PS is a diagonal matrix.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let P =Thena)P has two linearly independent eigenvectorsb)P has an eigen vectorc)P is non singulard)There exists a non singular matrix S such that S-1PS is a diagonal matrix.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Mathematics tests.

Explore Courses for Mathematics exam