Engineering Mathematics
Linear Algebra
Eigen Values and Eigen Vectors
Questions mapped to Eigen Values and Eigen Vectors under Linear Algebra.
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IncorrectTwo matrices and have a common eigenvalue 2, and the same corresponding nonzero eigenvector.
Which of the following options is/are correct?
(Note: is the identity matrix.)
Determinant
Determinant
Determinant
Determinant
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Sign in to UnlockLet and be the two eigenvectors corresponding to distinct eigenvalues of a real symmetric matrix. Which one of the following statements is true?
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Sign in to UnlockThe sum of the eigenvalues of the matrix is ________ (rounded off to the nearest integer).
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Sign in to Unlockdenotes the exponential of a square matrix . Suppose is an eigen value and is the corresponding eigen-vector of matrix .
Consider the following two statements:
Statement 1: is an eigen value of .
Statement 2: is an eigen-vector of .
Which one of the following options is correct?
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Sign in to UnlockLet and be real numbers such that .
The eigenvalues of the matrix are
pq and –pq
1 and 1
and
1 and -1
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Sign in to UnlockM is a 2 × 2 matrix with eigenvalues 4 and 9. The eigenvalues of are
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Sign in to UnlockThe eigen values of the matrix given below are
.
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Sign in to UnlockThe matrix has three distinct eigenvalues and one of its eigenvectors is . Which one of the following can be another eigenvector of A?
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Sign in to UnlockConsider a matrix with every element being equal to 1. Its only non-zero Eigen value is ___________.
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Sign in to UnlockLet the Eigen values of a matrix A be 1, -2 with eigenvectors and respectively. Then the Eigen values and eigenvectors of the matrix would, respectively, be
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Sign in to UnlockLet A be a real matrix with rank 2. Which one of the following statement is TRUE?
Rank of is less than 2
Rank of is equal to 2
Rank of is greater than 2
Rank of can be any number between 1 and 3
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Sign in to UnlockA matrix P is such that, . Then the eigenvalues of P are
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Sign in to UnlockLet . Consider the set S of all vectors such that where . Then S is
a circle of radius
a circle of radius
an ellipse with major axis along
an ellipse with minor axis along
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Sign in to UnlockThe maximum value of ‘a’ such that the matrix has three linearly independent real eigenvectors is
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Sign in to UnlockA system matrix is given as follows.
The absolute value of the ratio of the maximum Eigen value to the minimum Eigen value is ______________.
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Sign in to UnlockWhich one of the following statements is true for all real symmetric matrices?
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Sign in to UnlockA matrix has Eigen values –1 and -2. The corresponding eigenvectors are and respectively. The matrix is
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Sign in to UnlockAn eigenvector of is
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Sign in to UnlockThe trace and determinant of a 2 × 2 matrix are known to be -2 and -35 respectively. Its Eigen values are
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Sign in to Unlockis an n-tuple nonzero vector. The n × n matrix
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Sign in to UnlockThe linear operation L(x) is defined by the cross product , where and are three dimensional vectors. The 3×3 matrix M of this operation satisfies
Then the Eigen values of M are
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Sign in to UnlockFor the matrix , one of the Eigen values is equal to –2. Which of the following is an Eigen vector?
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Sign in to UnlockThe vector is an Eigen vector of . One of the given values of A is:
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Sign in to UnlockThe sum of the Eigen values of the matrix A is:
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Sign in to UnlockGiven the matrix. Its Eigen values are ____________.
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Sign in to UnlockThe eigen-values of the matrix are
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