If the system
2x – y + 3z = 2
x + y + 2z = 2
5x – y + az = b
Has infinitely many solutions, then the values of a and b, respectively, are
For what value of μ do the simultaneous equations 5x + 7y = 2, 15x + 21y = μ have no solution?
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GaussSeidel method is used to solve the following equations (as per the given order):
x_{1} + 2x_{2} + 3x_{3} = 5
2x_{1} + 3x_{2} + x_{3} = 1
3x_{1} + 2x_{2} + x_{3} = 3
Assuming initial guess as x_{1} = x_{2} = x_{3} = 0, the value of x_{3} after the first iteration is ________
The value of k, for which the following system of linear equations has a nontrivial solution.
x + 2y  3z = 0
2x + y + z = 0
x  y + kz = 0
For what value of λ, do the simultaneous equation 2x + 3y = 1, 4x + 6y = λ have infinite solutions?
For what value of k, the system linear equation has no solution
(3k + 1)x + 3y  2 = 0
(k^{2} + 1)x + (k  2)y  5 = 0
The value of k for which the system of equations x + ky + 3z = 0, 4x + 3y + kz = 0, 2x + y + 2z = 0 has nontrivial solution is
Consider matrix The number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________
The set of equations
x + y + z = 1
ax – ay + 3z = 5
5x – 3y + az = 6
has infinite solutions, if a =
Consider the system of equations The value of x_{3} (round off to the nearest integer), is ______.
The approximate solution of the system of simultaneous equations
2x  5y + 3z = 7
x + 4y  2z = 3
2x + 3y + z = 2
by applying GaussSeidel method one time (using initial approximation as x  0, y  0, z  0) will be:
A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ 0. Will it be possible to solve for x and obtain a unique solution by multiplying both left and right sides of the equation by A^{T} (the super script T denotes the transpose) and inverting the matrix A^{T} A?
Consider a matrix
The matrix A satisfies the equation 6A^{1} = A^{2} + cA + dI, where c and d are scalars and I is the identity matrix. Then (c + d) is equal to
The system of linear equations
y + z = 0
(4d  1) x + y + Z = 0
(4d  1) z = 0
has a nontrivial solution, if d equals
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406 videos217 docs164 tests
