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Let ω be a complex number such that ω3 = 1 but ω ≠ 1.
If A =
, then which of the following statementare true?
If A =
, then which of the following statementare true?- a)A is invertible
- b)rank (A) = 1
- c)1 is an eigen value of A
- d)rank(A ) = 2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Let ω be a complex number such that ω3 = 1 but ω &ne...
Determinant of Matrix A = 0 so it is not invertible.
Since determinant of matrix is zero it eigen value is zero.
After converting the matrix into row echlon form we find that there exist only 1 non zero row hence the rank of the matrix is 1.
Since determinant of matrix is zero it eigen value is zero.
After converting the matrix into row echlon form we find that there exist only 1 non zero row hence the rank of the matrix is 1.
Most Upvoted Answer
Let ω be a complex number such that ω3 = 1 but ω &ne...
We are given that the matrix
where ω be a complex number such that ω3 = 1, but ω ≠ 1
Applying the operations C3 --> C1 + C2 + C3 this operation yields.
∴ Rank of A = 2 ( ∵ 1+ ω + ω2 = 0)
where ω be a complex number such that ω3 = 1, but ω ≠ 1
Applying the operations C3 --> C1 + C2 + C3 this operation yields.
∴ Rank of A = 2 ( ∵ 1+ ω + ω2 = 0)
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Let ω be a complex number such that ω3 = 1 but ω ≠ 1.If A =,then which of the following statementare true?a)A is invertibleb)rank (A) = 1c)1 is an eigen value of Ad)rank(A ) = 2Correct answer is option 'B'. Can you explain this answer?
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