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Let  Let M be the matrix whose columns are, V1+V2, 2V1 + V2, V1 - 2V2 in that order. Then which of the followings is not true for Matrix M ?
  • a)
    M is not invertible.
  • b)
    M has all distinct eigenvalues
  • c)
    The no. of linearly independent solution’s of the system of linear equation' Mx = 0 is 1.
  • d)
    M is not diagonalizable.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
LetLet M be the matrix whose columns are, V1+V2,2V1 + V2, V1 - 2V2 in ...
Given
det M = 2 + 12 + 3 - ( 2 + 12 + 3) = 0
⇒ M not invertible.
Characteristic equation of M is given as :
T ake Mx = 0 ...(i)
Then we know no. of L.l. solution of (i) = nullity of M
= no. of column's of M - Rank M = 3 - 2 = 1
Since all the ev’s of M are distinct.
⇒ M is diagonalizable.
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Most Upvoted Answer
LetLet M be the matrix whose columns are, V1+V2,2V1 + V2, V1 - 2V2 in ...
Given
det M = 2 + 12 + 3 - ( 2 + 12 + 3) = 0
⇒ M not invertible.
Characteristic equation of M is given as :
T ake Mx = 0 ...(i)
Then we know no. of L.l. solution of (i) = nullity of M
= no. of column's of M - Rank M = 3 - 2 = 1
Since all the ev’s of M are distinct.
⇒ M is diagonalizable.
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LetLet M be the matrix whose columns are, V1+V2,2V1 + V2, V1 - 2V2 in that order. Then which of the followings is not true for Matrix M ?a)M is not invertible.b)M has all distinct eigenvaluesc)The no. of linearly independent solution’s of the system of linear equation Mx = 0 is 1.d)M is not diagonalizable.Correct answer is option 'D'. Can you explain this answer?
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LetLet M be the matrix whose columns are, V1+V2,2V1 + V2, V1 - 2V2 in that order. Then which of the followings is not true for Matrix M ?a)M is not invertible.b)M has all distinct eigenvaluesc)The no. of linearly independent solution’s of the system of linear equation Mx = 0 is 1.d)M is not diagonalizable.Correct answer is option 'D'. 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 LetLet M be the matrix whose columns are, V1+V2,2V1 + V2, V1 - 2V2 in that order. Then which of the followings is not true for Matrix M ?a)M is not invertible.b)M has all distinct eigenvaluesc)The no. of linearly independent solution’s of the system of linear equation Mx = 0 is 1.d)M is not diagonalizable.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for LetLet M be the matrix whose columns are, V1+V2,2V1 + V2, V1 - 2V2 in that order. Then which of the followings is not true for Matrix M ?a)M is not invertible.b)M has all distinct eigenvaluesc)The no. of linearly independent solution’s of the system of linear equation Mx = 0 is 1.d)M is not diagonalizable.Correct answer is option 'D'. Can you explain this answer?.
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