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Let T: R3 → R3 be the Linear transformation whose matrix with respect to the standard basis  Then T 
  • a)
     has distinct eigenvalues
  • b)
     has a non-zero null space 
  • c)
     has eigenvectors that span R3
  • d)
     maps the subspace spanned by e1 and e2 into it self 
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let T: R3→ R3be the Linear transformation whose matrix with respe...
Let T : R3 + R3
such that the matrix for T is given by 
First we check out the eigenvalues of A is given by 
The Eigen vectors for l =1 is u1 = 
as 
and Eigen vectors for λ = –2 are v2 = 
and if P = 
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Let T: R3→ R3be the Linear transformation whose matrix with respect to the standard basisThen Ta)has distinct eigenvaluesb)has a non-zero null spacec)has eigenvectors that span R3d)maps the subspace spanned by e1and e2into it selfCorrect answer is option 'C'. Can you explain this answer?
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Let T: R3→ R3be the Linear transformation whose matrix with respect to the standard basisThen Ta)has distinct eigenvaluesb)has a non-zero null spacec)has eigenvectors that span R3d)maps the subspace spanned by e1and e2into it selfCorrect answer is option 'C'. 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 T: R3→ R3be the Linear transformation whose matrix with respect to the standard basisThen Ta)has distinct eigenvaluesb)has a non-zero null spacec)has eigenvectors that span R3d)maps the subspace spanned by e1and e2into it selfCorrect answer is option 'C'. 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 T: R3→ R3be the Linear transformation whose matrix with respect to the standard basisThen Ta)has distinct eigenvaluesb)has a non-zero null spacec)has eigenvectors that span R3d)maps the subspace spanned by e1and e2into it selfCorrect answer is option 'C'. Can you explain this answer?.
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