Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > For the matrix P =, one of the eigen values i...
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For the matrix P = 
, one of the eigen values is - 2. Which of the following is an eigen vector?
, one of the eigen values is - 2. Which of the following is an eigen vector?- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
For the matrix P =, one of the eigen values is - 2. Which of the follo...
We know that AX = λX
AX − λX = [0]
(A − λI)X = [0] ----> (1) where I =
Identity matrix.
AX − λX = [0]
(A − λI)X = [0] ----> (1) where I =
Identity matrix.
Given that λ = −2
Now, from the equation (1),
(A − λI)X = [0]
(A − λI)X = [0]
Now, we can apply some operation on matrix
Again apply some operation on matrix
In R3, we create Nullity. So Rank of this matrix is 2 [Rank:Maximum number of independent Rows/Colums]
r = 2, and number of unknowns (Variables = 3)
Here clearly see, r < n
So, there are Infinitely many solution are possible, and n − r = 3 − 2 = 1 variable give some value and other will be evaluate accordingly.
r = 2, and number of unknowns (Variables = 3)
Here clearly see, r < n
So, there are Infinitely many solution are possible, and n − r = 3 − 2 = 1 variable give some value and other will be evaluate accordingly.
Let say y = k
z = 0 ----> (2)
5x − 2k + 2z = 0
5x − 2k + 0 = 0
5x = 2k
z = 0 ----> (2)
5x − 2k + 2z = 0
5x − 2k + 0 = 0
5x = 2k
x = 2k/3
Finally we got the Eigen Vector, X = 
Put the Value of k = 5
and we get, X =
Put the Value of k = 5
and we get, X =
Actually, we get Infinitely many number of solutions.
So, we can get Infinte number of Eigen Vector, but for k = 5, we got one Eigen Vector.
So, we can get Infinte number of Eigen Vector, but for k = 5, we got one Eigen Vector.
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For the matrix P =, one of the eigen values is - 2. Which of the following is an eigen vector?a)b)c)d)Correct answer is option 'D'. Can you explain this answer?
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For the matrix P =, one of the eigen values is - 2. Which of the following is an eigen vector?a)b)c)d)Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about For the matrix P =, one of the eigen values is - 2. Which of the following is an eigen vector?a)b)c)d)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For the matrix P =, one of the eigen values is - 2. Which of the following is an eigen vector?a)b)c)d)Correct answer is option 'D'. Can you explain this answer?.
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