Engineering Mathematics
Linear Algebra
Matrices and Determinants
Questions mapped to Matrices and Determinants under Linear Algebra.
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Incorrectis an skew-symmetric matrix with real-valued entries, and is an -dimensional column vector with real-valued entries such that .
The quantity evaluates to
(Answer in integer)
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Sign in to UnlockConsider an orthogonal matrix with real entries and each column having unit Euclidean norm.
Which of the following statements is/are correct?
The value of the determinant of is either +1 or -1
The eigenvalues of have modulus 1
, for all , where denotes the Euclidean norm of , and , for all distinct
, for all , where denotes the Euclidean norm of , and , for all
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Sign in to UnlockLet and let I can be identity matrix. Then is equal to
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Sign in to UnlockWhich one of the following matrices has an inverse?
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Sign in to UnlockFor a given vector , the vector normal to the plane defined by is
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Sign in to UnlockIn the figure, the vectors and are related as: by a transformation matrix A. The correct choice of is
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Sign in to UnlockConsider a matrix whose -th element, . Then the matrix will be
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Sign in to UnlockConsider a matrix . The matrix satisfies the equation , where and are scalars and is the identity matrix. Then is equal to
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Sign in to UnlockLet be a matrix such that is null matrix, and let be the identity matrix. The determinant of is _______.
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Sign in to UnlockThe number of purely real elements in a lower triangular representation of the given matrix, obtained through the given decomposition is
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Sign in to UnlockThe rank of the matrix, is __________________.
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Sign in to UnlockConsider a matrix , where, and are the column vectors. Suppose , where and are the row vectors. Consider the following statements:
Statement 1:
Statement 2:
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Sign in to UnlockConsider a non-singular square matrix A If and, the determinant of the matrix A is ________ (up to 1 decimal place).
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Sign in to UnlockLet and, where I is identity matrix. The determinant of B is ______ (up to 1 decimal place).
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Sign in to UnlockLet and . The value of equals _________. (Give the answer up to three decimal places)
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Sign in to UnlockIf the sum of the diagonal elements of a 2 x 2 matrix is -6, then the maximum possible value of determinant of the matrix is ____________.
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Sign in to UnlockTwo matrices A and B are given below:
If the rank of matrix A is N, then the rank of matrix B is
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Sign in to UnlockGiven that
and , the value of is
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Sign in to UnlockThe matrix is decomposed into a product of a lower triangular matrix [L] and an upper triangular matrix [U]. The properly decomposed [L] and [U] matrices respectively are
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Sign in to UnlockThe characteristic equation of a (3 × 3) matrix P is defined as. If I denote identity matrix, then the inverse of matrix P will be
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Sign in to UnlockIf the rank of a (5×6) matrix Q is 4, then which one of the following statements is correct?
Q will have four linearly independent rows and four linearly Independent columns
Q will have four linearly Independent rows and five linearly Independent columns
will be invertible
will be invertible
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Sign in to UnlockA is a m×n full ran matrix with m > n and I is an identity matrix. Let matrix. Then, which one of the following statements is FALSE?
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Sign in to UnlockLet P be a 2 ´ 2 real orthogonal matrix and is a real vector with length. Then, which one of the following statements is correct?
where at least one vector satisfies
for all vectors
where at least one vector satisfies
No relationship can be established between and
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Sign in to UnlockLet x and y be two vectors in a 3 dimensional space and <x, y> denote their dot product. Then the determinant
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Sign in to UnlockCayley-Hamilton Theorem states that a square matrix satisfies its own characteristic equation.
Consider a matrix
A satisfies the relation
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Sign in to UnlockCayley-Hamilton Theorem states that a square matrix satisfies its own characteristic equation.
Consider a matrix
equals
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Sign in to Unlockare three vectors
An orthogonal set of vectors having a span that contains p, q, r is
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Sign in to Unlockare three vectors
The following vector is linearly dependent upon the solution to the previous problem
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Sign in to UnlockIf , the top row of is:
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Sign in to UnlockThe determinant of the matrix
is:
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Sign in to UnlockThe inverse of A is:
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Sign in to UnlockA square matrix is called singular, if its
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Sign in to UnlockExpress the given matrix A as a product of two triangular matrices, L and U, where the diagonal elements of the lower triangular matrix L are unity and U is an upper triangular matriX
None
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Sign in to UnlockThe inverse of the matrix is:
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Sign in to Unlockmatrix has all its entries equal to -1. The rank of the matrix is
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