A system of equations [A][X]=[B][A][X]=[B] It has Unique solution if rank(A)=(A)= rank(A|B)=(A|B)= number of unknowns; It has Infinite solutions if rank(A)=(A)= rank(A|B)<(A|B)< number of unknowns; It has No solution (i.e. inconsistent) if rank(A)<(A)<...
A system of equations [A][X]=[B][A][X]=[B] It has Unique solution if rank(A)=(A)= rank(A|B)=(A|B)= number of unknowns; It has Infinite solutions if rank(A)=(A)= rank(A|B)<(A|B)< number of unknowns; It has No solution (i.e. inconsistent) if rank(A)<(A)<...
Answer to: True or False: If a system of linear equation of two variables has a unique solution, then the representing lines of their equations are...
<p>To determine the condition under which the given system of equations has a non-trivial solution, we need to analyze the coefficient matrix and its determinant. The system of equations is as follows:</p><p>1. \( x + y + z = 0 \) 2. \( ax + by + z = 0 \
Since this equation has complex coefficients, though still formally simple, the problem of checking the sign of the real parts of the two roots becomes more complicated. The instability of waves against long wavelength longitudinal modes is often called the Benjamin–Feir instability though this insta...
4. Infinite Sum of the Contour Integral Again, we use the method in [8]. Using Equation (2) replace y by log(𝑎)+2𝜋(𝑦+1) and multiply both sides by (−1)𝑦𝑒2𝜋𝑚(𝑦+1). Next, we take the infinite sum over 𝑦∈[0,∞) and simplify in terms of the Lerch...
Multi-stability is a widely observed phenomenon in real complex networked systems, such as technological infrastructures, ecological systems, gene regulation, transportation and more. Thus, even if the system is at equilibrium in a normal functional stat
1), various concentrations of NaCl (99.998%, Alfa Aesar) solution were prepared in deionized water; the measured conductivity of these solutions corresponds to a background concentration of monovalent ions of c0 ≈ 5 μM. The ionic strength of the various electrolyte solutions in our ...
One can solve this system of equations for x and y. Let the solution be x1N and y1N. Compare these values with x1 and y1, respectively. If the two solutions are not close, substitute x=x1N and y=y1N and repeat the steps till convergence occurs. Fig. 1 shows a flowchart of this ...
1b,c. We use velocity fields that conserve fluid mass and satisfy the Navier–Stokes equation for a PVS of infinite length. These velocity fields are also valid for our finite tube because inertial effects are negligible and hence the entrance length for fully-developed flow is negligibly ...