Engineering Mathematics
Linear Algebra
Solution of Linear Equations
Questions mapped to Solution of Linear Equations under Linear Algebra.
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IncorrectWhich one of the following statements is ALWAYS correct about a collection of column vectors, each having real-valued entries?
If , then the column vectors must be linearly dependent
If , then the column vectors must be linearly independent
If , then the column vectors must be orthogonal
If , then the column vectors must be linearly independent
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Sign in to UnlockConsider the system of linear equations: , where is an matrix, and and are -dimensional column vectors.
Suppose this system of equations has a unique solution. Which of the following statements is/are correct?
exists
The system of equations also has a unique solution for
, for
, where denotes the augmented matrix.
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Sign in to UnlockConsider the set of points which minimize the real valued function
Which of the following statements is true about the set S?
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Sign in to UnlockLet , and . Then, the system of linear equations has
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Sign in to UnlockWe have a set of 3 linear equations in 3 unknowns. ‘X = Y’ means X and Y are equivalent statements and means X and Y are not equivalent statements.
P. There is a unique solution.
Q. The equations are linearly independent.
R. All Eigen values of the coefficient matrix are nonzero.
S. The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?
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Sign in to UnlockGiven a system of equations:
Which of the following is true regarding its solutions
The system has a unique solution for any given
The system will have infinitely many solutions for any given
Whether or not a solution exists depends on the given
The system would have no solution for any values of
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Sign in to UnlockThe equation has
No solution
Only one solution
Non-zero unique solution
Multiple solutions
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Sign in to UnlockFor the set of equations
The following statement is true:
Only the trivial solution exists.
There are no solutions.
A unique non-trivial solution exists
Multiple non-trivial solutions exist
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Sign in to UnlockIn the matrix equation Px = q, which of the following is a necessary condition for the existence of at least one solution for the unknown vector x:
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Sign in to UnlockA set of linear equations is represented by the matrix equation Ax=b the necessary condition for the existence of a solution for this system is:
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Sign in to UnlockGauss-Seidel iterative method can be used for solving a set of
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Sign in to UnlockA set of three linear equations with unknowns X, Y and Z is shown below
Decompose the coefficient matrix into an upper triangular matrix and then solve for the unknowns, X, Y and Z.
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Sign in to UnlockIf two vectors u and v in a plane are linearly independent, then, they cannot be collinear. ( True=1, False=0)
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Sign in to UnlockThe number of linearly independent solutions of the system of equations , is equal to _________________
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