(4) 6. Find all values of t for which the linear system in the variables z...
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
Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, do the following. (Use x, y, and z as your variables, each representing the columns in turn.)1006010−40013(a) Determine whether the system has a solution.The system has one solution.The system has infinitely many solutions. The system has no solution.(b) Find the solution or solutions to the system, if they exist. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your...
Problem 5 Consider the linear system [1 2 0 2 -4 7x(t) 1 -4 6 y(t) [1 -2 2] (t). (4) a(t = (a) Is the system (4) observable? (b) Give a basis for the unobservable subspace of the system (4). In the remainder of this problem, consider the linear system а — 3 8— 2а 0 1 2a u(t) (t) (5) x(t) = with a a real parameter. (c) Determine all values of a for which the system (5)...
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...
4. Use determinants to find all values of h such that the following linear system has exactly one solution for any b1,b2, bз, ba ER hx4 2x2 3 b2 + hxi 12x4 2хз + hx2 + I1 8x2 - Do not use Maple to calculate any determinants. You are permitted to use the formula for a 3 x 3 determinant Hint: The determinant will be a cubic polynomial in h. You must factor this polynomial. It is a fact h...
Problem 4. Linear Time-Invariant System.s A linear system has the block diagram y(t) z(t) →| Delay by 1 dt *h(t) where g(t) sinc(t Since this is a linear time invariant system, we can represent it as a convolution with a single impulse response h(t) a) Find the impulse response h(t). You don't need to explicitly differentiate. b) Find the frequency response H(j for this system.
- 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.
8) In the system of equations below, x and y are variables and t is a parameter: a) Find all the values of t such that the system has a unique solution. b) Solve for x and y using the inverse matrix method.
Find the augmented matrix of the linear system X +y+z= -8 X – 3y + 3z = -4 X – Y + 2z = -6. Use Gauss-Jordon elimination to transform the augmented matrix to its reduced row- echelon form. Then find the solution or the solution set of the linear system.
10. Determine the values of k for which the system of linear equations has (i) no solution vector, (ii) a unique solution vector, (iii) more than one solution vector (x, y, z): (a) kx+ y+ z= (b) 2x + (k-1)y + (3-k)2-1 2y + (k-3): = 2 x+ky + z = 1 -2y+ x 2x + ky- z =-2 (c) x + 2y + k= 1 (d) -3z =-3
10. Determine the values of k for which the system of...