(k) Find the value(s) of k such that the linear system X k has periodic solutions...
Linear Algebra Determine the value of k such that the system of linear equations has infinitely many solutions. x - y + 2z=0 - x + y - z = 0 X + ky + z = 0
Find a value of b such that the system of linear questions has infinitely many solutions: 6x + 2by = 3 4x + 2y = 2
Question 4. (20 pts.) a) In the following system of linear equations, find k such that the system Has unique solution Has infinitely many solutions Has no solution x+z=0 x + 2y + 2z = 3 (x + kk + 1)y + z = k Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix 13 2 6 1 -2 3 16 4 12 b) Find the Fourier series representation of the function with period 21 given by...
Find the value of k such that the system of linear equations is inconsistent.{4x-8y = -3{2x+ky = 16I know that the answer is k = -4 but I don't know how to solve to get that answer.
use linear algebra methods to solve only please 2. Find the value(s) of a (if they exist) for which the system of equations has: (a) No solution. (b) One unique solution. (c) Infinitely many solutions. x + y - z = 2 x + 2y + z = 3 2x + y - 4z = a
Exercise 5.27 Suppose and 2t) are solutions of a linear homogeneous system A (t)x with a coefficient matrix A(t) that is continuous on an interval a < t < β. Prove that the determinant s() -det( 3) (t) 2 is either never equal to 0 for α < t < β or else it is identically (i.e., alu ays) equal to 0 on α < t < β. (Hint: by direct calculation show the determinant satisfies the first order, linear...
4. For the system shown, find the value of K and a so that two of the closed-loop poles s+4 G(s)= (s+8Xs+2) + Y(s) X(s) K are at s-at ja. 4. For the system shown, find the value of K and a so that two of the closed-loop poles s+4 G(s)= (s+8Xs+2) + Y(s) X(s) K are at s-at ja.
Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values. x1+ax2−x3 = 2 −x1+4x2−2x3 = −5 −2x1+3x2+x3 = −4 No Solutions: Unique Solution: Infinitely Many Solutions:
Need this asap Thanks k 0 1 (c) Consider the matrix 0 k 2 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A- exist? iii. For what value(s) of k does the linear system Ai= have nontrivial solutions? iv. For what value(s) of k does A have zero as an eigenvalue? v. For any vector 5 € R", find the value(s) of k for which the linear system Až = b has a unique...
19. Solve the following linear system. If it has no solution or infinite solutions, so state: 3x- y- -x+2y-4