Eigen Values and Eigen Vectors
Trending Questions
Q. In the given matrix ⎡⎢⎣1−12010121⎤⎥⎦, one of the eigen value is 1. The eigen vectors corresponding to the eigen value 1 are
- α(4, 2, 1)|α≠0, αϵR
- α(−4, 2, 1)|α≠0, αϵR
- α(√2, 0, 1)|α≠0, αϵR
- α(−√2, 2, 1)|α≠0, αϵR
Q. For the matrix [4224], the eigen value corresponding to the eigen vector [101101] is
- 2
- 4
- 6
- 8
Q.
is equal to?
Q. The eigen values of the matrix given below are: ⎡⎢⎣0100010−3−4⎤⎥⎦
- (0, -1, -3)
- (0, -2, -3)
- (0, 2, 3)
- (0, 1, 3)
Q. The eigen values of the matrix [01−10] are
- i and -i
- 1 and -1
- 0 and 1
- 0 and -1
Q. The minimum eigen value of the following matrix is ⎡⎢⎣3525127275⎤⎥⎦
- 0
- 1
- 2
- 3
Q. Let P = [3113] Consider the set S of all vectors [xy] such that a2+b2 = 1 where (ab) = P(xy) then s is
- A circle of radius √10
- A circle of radius 1√10
- An ellipse with major axis along [11]
- An ellipse with minor axis along [11]
Q. Consider the 5 x 5 matrix A=⎡⎢
⎢
⎢
⎢
⎢
⎢⎣1234551234451233451223451⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
It is given that A has only one real eigen value. Then the real eigen value A is
It is given that A has only one real eigen value. Then the real eigen value A is
- -25
- 0
- 15
- 25
Q. The determinant of a 2 x 2 matrix is 50. If one eigen value of the matrix is10, the other eigen value is
Q. The eigen values of the matrix ⎡⎢
⎢
⎢⎣2−100030000−2000−14⎤⎥
⎥
⎥⎦ are
- 2, −2, 1, −1
- 2, 3, −2, 4
- 2, 3, 1, 4
- None
Q. The Eigen vectors of the matrix
[1−1−11] is/are
[1−1−11] is/are
- (1, 0)
- (0, 1)
- (1, 1)
- (1, −1)
Q. If A is 3×3 matrix and Trace A = 9, |A| = 24 and one of the eigen values is 3, then sum of other eigen values is __________.
- 5
- 8
- 6
- 9
Q. The eigen values of the matrix
[533−3] are:
[533−3] are:
- 6
- 5
- −3
- −4
Q. Consider the matrix P = ⎡⎢
⎢
⎢
⎢⎣1√201√2010−1√201√2⎤⎥
⎥
⎥
⎥⎦ which one of the following statements about P is INCORRECT?
- Determinant of P is equal to 1.
- P is orthogonal
- Inverse of P is equal to its transpose.
- All eigen values of P are real numbers
Q. A system matrix is given as follows :
A=⎡⎢⎣01−1−6−116−6−115⎤⎥⎦
The absolute value of the ratio of the maximum eigen value to the minimum eigen value is __
A=⎡⎢⎣01−1−6−116−6−115⎤⎥⎦
The absolute value of the ratio of the maximum eigen value to the minimum eigen value is __
- 0.333
Q. The lowest eigen value of the 2 x 2 matrix [4213] is .
- 2
Q. Consider the matrix:
P = ⎡⎢⎣110011001⎤⎥⎦
The number of distinct eigenvalues of P is:
P = ⎡⎢⎣110011001⎤⎥⎦
The number of distinct eigenvalues of P is:
- 3
- 0
- 1
- 2
Q. An eigen vector of P=⎡⎢⎣110022003⎤⎥⎦ is
- [−111]T
- [121]T
- [1−12]T
- [21−1]T
Q. The eigen values of the matrix A = ⎡⎢⎣1−150560−65⎤⎥⎦ are
- 1, 5, 6
- 1, -5, ±j6
- 1, 5±j6
- 1, 5, 5
Q.
What is the meaning of determinants?
Q. The eigen values of matrix [9558] are
- -2.42 and 6.86
- 3.48 and 13.53
- 4.70 and 6.86
- 6.86 and 9.50
Q. Consider a 2 x 2 square matrix A = [σXωσ]
Where x is unknown. If the eigen values of the matrix A are (σ+jω) and (σ−jω), then x is equal to
Where x is unknown. If the eigen values of the matrix A are (σ+jω) and (σ−jω), then x is equal to
- +jω
- -jω
- +ω
- -ω
Q. [1, 1, 2] is an eigen vector of the matrix, A=⎡⎢⎣31−122−1220⎤⎥⎦ corresponding to the eigen value x. The value of x is _______ .
- 2
Q. The vector ⎡⎢⎣12−1⎤⎥⎦ is an eigen vector of A=⎡⎢⎣−22−321−6−1−20⎤⎥⎦. The corresponding eigen value of A is _____.
- 1
- 2
- 5
- −1
Q. The matrix [2−44−2] has
- Real eigen values and eigen vectors
- Real eigen values but complex eigen vectors
- Complex eigen values but real eigen vectors
- Complex eigen values and eigen vectors
Q. In matrix equation [A] {X} = {R},
[A] = ⎡⎢⎣484816−44−415⎤⎥⎦, {X}=⎧⎪⎨⎪⎩214⎫⎪⎬⎪⎭ and {R}=⎧⎪⎨⎪⎩321664⎫⎪⎬⎪⎭
One of the eigen values of matrix [A] is
[A] = ⎡⎢⎣484816−44−415⎤⎥⎦, {X}=⎧⎪⎨⎪⎩214⎫⎪⎬⎪⎭ and {R}=⎧⎪⎨⎪⎩321664⎫⎪⎬⎪⎭
One of the eigen values of matrix [A] is
- 16
- 8
- 15
- 4
Q. Let the Eigen vector of the matrix [1202] be written in the form [1a] and [1b]. What is the value of (a + b)?
- 0
- 12
- 1
- 2
Q. A 2 x 2 matrix M has eigen values 2 & 3 with eigen vectors [21]&[12] respectively. The sum of all elements of Matrix M is _______.
- 5
Q. M is a 2×2 matrix with eigen values 2 and 5.The eigen values of M−1are
- -2 and -5
- 2 and 5
- 0.5 and 0.2
- Can't be determined
Q. One of the eigen value for the following matrix is
[x28x]
[x28x]
- x - 4
- - x - 4
- 4
- -4