The system of linear equations
4x + 2y = 7
2x + y = 6 has
For the following set of simultaneous equations:
1.5x – 0.5y = 2
4x + 2y + 3z = 9
7x + y + 5z = 10
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The following set of equations has
3 x + 2 y + z = 4
x – y + z = 2
2 x + 2 z = 5
Consider the system of simultaneous equations
x + 2y + z = 6
2x + y + 2z = 6
x + y + z = 5
This system has
Multiplication of matrices E and F is G. Matrices E and G are
What is the matrix F?
Consider a nonhomogeneous system of linear equations representing mathematically an overdetermined system. Such a system will be
For the set of equations
x_{1} + 2x + x_{3} + 4x_{4} = 0
3x_{1} + 6x_{2} + 3x_{3} + 12x_{4} = 0
Let P ≠ 0 be a 3 × 3 real matrix. There exist linearly independent vectors x and y such that Px = 0 and Py = 0. The dimension of the range space of P is
The eigen values of a skewsymmetric matrix are
The rank of a 3×3 matrix C (=AB), found by multiplying a nonzero column matrix Aof size 3×1 and a nonzero row matrix B of size 1×3, is
Match the items in columns I and II.
Column I Column II
P. Singular matrix 1. Determinant is not defined
Q. Nonsquare matrix 2. Determinant is always one
R. Real symmetric 3. Determinant is zero
S. Orthogonal matrix 4. Eigenvalues are always real
5. Eigenvalues are not defined
Real matrices are given. Matrices [B] and
[E] are symmetric.
Following statements are made with respect to these matrices.
1. Matrix product [F]^{T} [C]^{T} [B] [C] [F] is a scalar.
2. Matrix product [D]^{T} [F] [D] is always symmetric.
With reference to above statements, which of the following applies?
The product of matrices (PQ)^{–1} P is
The matrix A
=
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
The inverse of the matrix is
The inverse of the 2 × 2 matrix is,
For what value of λ, do the simultaneous equation 2x + 3y = 1, 4x + 6y = λ have infinite solutions?
The Fourier transform of x(t) = e^{–at} u(–t), where u(t) is the unit step function.
Given that F(s) is the onesided Laplace transform of f(t), the Laplace transform of is [EC:
If f(t) is a finite and continuous function for t, the Laplace transformation is given by
For f(t) = cos h mt, the Laplace transformation is…..
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65 videos121 docs94 tests
