Leta real symmetric matrix.Pis the orthogonal matrix such thatP-1 APis a diagonal matrix given byFind the value ofandalpha;Correct answer is '6'. Can you explain this answer?

EduRev

All Courses

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

Physics Exam > Physics Questions > Leta real symmetric matrix.Pis the orthogonal...

Join the Discussion on the App

Let

a real symmetric matrix. P is the orthogonal matrix such that P^-1 AP is a diagonal matrix given by

Find the value of α

Correct answer is '6'. Can you explain this answer?

FREE This question is part of

Linear Algebra NAT Level - 2

Attempt Test

Attempt this Test

Verified Answer

Leta real symmetric matrix.Pis the orthogonal matrix such thatP-1 APis...

tr(A) = 7 ; |A| = 6
∴ The characteristic equation will be

⇒ λ = 6, 1 are the eigenvalues of A.
Now, Let (x, y) be the eigenvector corresponding to λ = 6, then,

i.e., –4x – 2y = 0
or 2x + y = 0
A non zero solution is u₁ = (1, –2)
Now, again if (x, y) is the eigenvector corresponding to λ = 1. Then

i.e., x – 2y = 0

A non-zero solution is u₂ = (2, 1)
Now, u₁ and u₂ will be orthogonal. Normalising u₁and u₂ yield the orthonormal vectors,

such that

The correct answer is: 6

View all questions of this test

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for Physics exam

Similar Physics Doubts

Let A be a 3 × 3 matrix. Suppose that the eigenvalues of A are –1, 0, 1 with respective eigenvectors (1,–1,0)T, (1,1,–2)T & (1,1,1)T. Then 6A is given byFind the value ofα Correct answer is '5'. Can you explain this answer?

View answer

In an one - dimensional harmonic oscillator , are respectively the ground, second and forth excited states. These three states are normalized and are orthogonal to one another.ψ1and ψ2 are two states defined by

View answer

If one of the eigen vector of Matrix A is [ 111 111 111] corresponding to the eigen value 0 is column matrix [ 0 1 -1 ] then the other orthogonal eigen vector for same eigen value is?

View answer

Find the orthogonal trajectory of the family of curves,y2=x3– 2so, find the value ofyas x→∞. Correct answer is '1'. Can you explain this answer?

View answer

Matrix A=(1 -1 2 3) then find the eigen value of matrix b=A^4-3A^3+3A^2-2A+8I?

View answer

Leta real symmetric matrix.Pis the orthogonal matrix such thatP-1 APis a diagonal matrix given byFind the value ofαCorrect answer is '6'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
Leta real symmetric matrix.Pis the orthogonal matrix such thatP-1 APis a diagonal matrix given byFind the value ofαCorrect answer is '6'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Leta real symmetric matrix.Pis the orthogonal matrix such thatP-1 APis a diagonal matrix given byFind the value ofαCorrect answer is '6'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Leta real symmetric matrix.Pis the orthogonal matrix such thatP-1 APis a diagonal matrix given byFind the value ofαCorrect answer is '6'. Can you explain this answer?.

Solutions for Leta real symmetric matrix.Pis the orthogonal matrix such thatP-1 APis a diagonal matrix given byFind the value ofαCorrect answer is '6'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics. Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.

Here you can find the meaning of Leta real symmetric matrix.Pis the orthogonal matrix such thatP-1 APis a diagonal matrix given byFind the value ofαCorrect answer is '6'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Leta real symmetric matrix.Pis the orthogonal matrix such thatP-1 APis a diagonal matrix given byFind the value ofαCorrect answer is '6'. Can you explain this answer?, a detailed solution for Leta real symmetric matrix.Pis the orthogonal matrix such thatP-1 APis a diagonal matrix given byFind the value ofαCorrect answer is '6'. Can you explain this answer? has been provided alongside types of Leta real symmetric matrix.Pis the orthogonal matrix such thatP-1 APis a diagonal matrix given byFind the value ofαCorrect answer is '6'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Leta real symmetric matrix.Pis the orthogonal matrix such thatP-1 APis a diagonal matrix given byFind the value ofαCorrect answer is '6'. Can you explain this answer? tests, examples and also practice Physics tests.

Explore Courses for Physics exam