GATE Exam  >  GATE Questions  >  Consider the matrix Which one of the followin... Start Learning for Free
Consider the matrix    Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix? 
  • a)
    Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists. 
  • b)
    Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist. 
  • c)
    Eigenvalue 3 has a multiplicity of 2, and no independent eigenvector exists. 
  • d)
    Eigenvalues are 3 and -3, and two independent eigenvectors exist.
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Consider the matrix Which one of the following statements is TRUE for ...
Characteristic equations is λ2 − 6λ + 9 = 0 ⇒ λ = 3, 3
Eigen value 3 has multiplicity 2.
Eigen vectors corresponding to λ = 3 is ( A − 3I ) X = 0
Number of linearly independent eigen vectors corresponding to eigen value λ = 3 is   n-r=2-1=1   where n= no. of unknowns, r= rank of (A − λI)
∴ One linearly independent eigen vector exists corresponding to λ = 3
View all questions of this test
Explore Courses for GATE exam
Consider the matrix Which one of the following statements is TRUE for theeigenvalues and eigenvectors of this matrix?a)Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists.b)Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist.c)Eigenvalue 3 has a multiplicity of 2, and no independent eigenvector exists.d)Eigenvalues are 3 and -3, and two independent eigenvectors exist.Correct answer is option 'A'. Can you explain this answer?
Question Description
Consider the matrix Which one of the following statements is TRUE for theeigenvalues and eigenvectors of this matrix?a)Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists.b)Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist.c)Eigenvalue 3 has a multiplicity of 2, and no independent eigenvector exists.d)Eigenvalues are 3 and -3, and two independent eigenvectors exist.Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the matrix Which one of the following statements is TRUE for theeigenvalues and eigenvectors of this matrix?a)Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists.b)Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist.c)Eigenvalue 3 has a multiplicity of 2, and no independent eigenvector exists.d)Eigenvalues are 3 and -3, and two independent eigenvectors exist.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the matrix Which one of the following statements is TRUE for theeigenvalues and eigenvectors of this matrix?a)Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists.b)Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist.c)Eigenvalue 3 has a multiplicity of 2, and no independent eigenvector exists.d)Eigenvalues are 3 and -3, and two independent eigenvectors exist.Correct answer is option 'A'. Can you explain this answer?.
Solutions for Consider the matrix Which one of the following statements is TRUE for theeigenvalues and eigenvectors of this matrix?a)Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists.b)Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist.c)Eigenvalue 3 has a multiplicity of 2, and no independent eigenvector exists.d)Eigenvalues are 3 and -3, and two independent eigenvectors exist.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE. Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of Consider the matrix Which one of the following statements is TRUE for theeigenvalues and eigenvectors of this matrix?a)Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists.b)Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist.c)Eigenvalue 3 has a multiplicity of 2, and no independent eigenvector exists.d)Eigenvalues are 3 and -3, and two independent eigenvectors exist.Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Consider the matrix Which one of the following statements is TRUE for theeigenvalues and eigenvectors of this matrix?a)Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists.b)Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist.c)Eigenvalue 3 has a multiplicity of 2, and no independent eigenvector exists.d)Eigenvalues are 3 and -3, and two independent eigenvectors exist.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Consider the matrix Which one of the following statements is TRUE for theeigenvalues and eigenvectors of this matrix?a)Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists.b)Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist.c)Eigenvalue 3 has a multiplicity of 2, and no independent eigenvector exists.d)Eigenvalues are 3 and -3, and two independent eigenvectors exist.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Consider the matrix Which one of the following statements is TRUE for theeigenvalues and eigenvectors of this matrix?a)Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists.b)Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist.c)Eigenvalue 3 has a multiplicity of 2, and no independent eigenvector exists.d)Eigenvalues are 3 and -3, and two independent eigenvectors exist.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Consider the matrix Which one of the following statements is TRUE for theeigenvalues and eigenvectors of this matrix?a)Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists.b)Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist.c)Eigenvalue 3 has a multiplicity of 2, and no independent eigenvector exists.d)Eigenvalues are 3 and -3, and two independent eigenvectors exist.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
Explore Courses for GATE exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev