GATE CS 2022 Set 1 — Question 53
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Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors
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Question
Which of the following is/are the eigenvector(s) for the matrix given below?
Correct answer
(A) pmatrix -1 \ 1 \ 0 \ 1 pmatrix; (C) pmatrix -1 \ 0 \ 2 \ 2 pmatrix; (D) pmatrix 0 \ 1 \ -3 \ 0 pmatrix
Solution
Let be the given matrix. We check for each option.(A) :
Row 1:
Row 2:
Row 3:
Row 4:
Result is . Eigenvector with .(B) :
Row 1: . Not an eigenvector.(C) :
Row 1:
Row 2:
Row 3:
Row 4:
Result is . Eigenvector with .(D) :
Row 1:
Row 2:
Row 3:
Row 4:
Result is . Eigenvector with .
Row 1:
Row 2:
Row 3:
Row 4:
Result is . Eigenvector with .(B) :
Row 1: . Not an eigenvector.(C) :
Row 1:
Row 2:
Row 3:
Row 4:
Result is . Eigenvector with .(D) :
Row 1:
Row 2:
Row 3:
Row 4:
Result is . Eigenvector with .
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