c) For what values of 2. does the following set of equations have non trivial solutions...
2. Find non-trivial (non-zero) product solutions for each of the following homogeneous bound ary value problems: 11(0.1) = 0, 14(r,t) = 0, 1 〉 0 t 〉 0 (a) 14-14x = 0, 0〈x〈L, t > 0 a(0.1) 0, 14(T.t)+γ.11(T,t)-O, t > 0 t>O, γǐs constant. 2. Find non-trivial (non-zero) product solutions for each of the following homogeneous bound ary value problems: 11(0.1) = 0, 14(r,t) = 0, 1 〉 0 t 〉 0 (a) 14-14x = 0, 0〈x〈L, t >...
Ax=O Unique solution (trivial solution x-0) No free variables Infinitely many (nontrivial) solutions Some free variables Every column of A is pivot column | (=> rank(A) = # of columns of A Some columns of A are not pivot columns rank(A)< #of columns of A You can use the above figure to answer the following questions are about homogeneous systems Ax-0. Answer TRUE or FALSE. If the answer is FALSE, choose FALSE with the appropriate counterexample, i.e example that shows...
9.14 Theorem. f the natural mumber N is a perfect square, then the Pell equation Ny 1 has no non-trivial integer solutions. After all this talk about trivial solutions, let's at least confirm that in some cascs non-trivial solutions do cxist. 9.15 Exercise. Find, by trial and error at least two non-trivial solutions to each of the Pell equations x2-2y2 I and x-3y21 Rolstcred by the cxistence of solutions for N 2 and N 3, our focus from this point...
Find all values of a, for which the system of linear equations does not have any solution. 2x + (9a² – 2)y = 3a x + y = 1
1 -2 10 (3) For which c does the system with augmented coefficient matrix 1 -3 3 0 have non- 2-5 c20 trivial solutions? In the case(s) there are non-trivial solutions, express them as a linear com- bination of basic solutions.
1. Find general solutions to the following differential systems of equations using dsolve: a. x' = y + t, y' = 2 -x+t b. x'=s-X, y' = -y - 3x, C. X" = x - x - y, y = -x- y - y - s', s" = -95 d. Solve the equations in c. above with the initial conditions x(0) = 1, x'(0) = 0, y(0) = -1, y'(0) = 0, $(0) = 1, s'(0) = 0, and plot...
- Tll Find values of a, b, and a much that the system of linear equations has (i) no solution, (ii) exactly une solution, and (iii) infinitely many solutions. 0 { x + 2y = 3 1. (ax+by = -9 @ S2X - Y + Z-a 1 x + y +22=b | 3x + 37=C.
Question 13 For what values of a does the system below have nontrivial solutions? 3x+3y-2z=0 -6x+ay+4z=0 2x+4y +4z=0 a) -4 b) 06 c) -2 d) 2 e) 3 f) None of the above. Review Later
For what values of m and n the following system of linear equations has no solution? ( 3x + y + 22 =2 3-2x+2y=3z = 1 (x -y + mzan a) m= &n=- b) m = 2 & n - 1 2 d) m= & ner c) m &nER
Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations below. 4x1 +4x2+8X3 = 16 - 12X1 - 12X2 - 24x3 = - 48 - 6x2 - 6x3 = 18 4x7 +4x2+8X3 = 0 - 12X1 - 12X2 - 24x3 = 0 - 6x2 - 6x3 = 0 X1 Describe the solution set, x = X2 of the first system of equations...