Find all solutions of the system of equations 2x + 2y + 2z = 4 2y...
5. Consider the system of equations: 2 - Y + 2z = 4 3x - 2y + 92 = 14 2. - 4y + az = b. Find all the values of a and b so that the system has a) no solution b) 1 solution e) exactly 3 solutions and 4) infinitely many solutions.
Question 1 (8 marks) Consider the linear system x - 2y + 2z = -1 -2x + 3y + kz=1 2x + ky + (k - 4)2 = 1 (a) For which values of k is this system (i) consistent or (ii) inconsistent? (b) Find all solutions to the system when k = -1. (c) Describe your answer to (b) geometrically.
1. Solve the following system of equations using Gauss-Jordan elimination. 3x - 2y +4z=3 2x +2y-2z=4 x+4y- &z=1
4. Find the complete solution to the system 2y z t = 1 2x - y - z -t = 3 3x 2z - 2t = -2
Solve the following system of equations. (Enter your answers as a comma-separated list. If there are infinitely many solutions, enter a parametric solution using t and/or s. If there is no solution, enter NONE.) 3y + 2z 4 2x-y-3z 2 2x 2y z6 (x, y, 2) Solve the following system of equations. (Enter your answers as a comma-separated list. If there are infinitely many solutions, enter a parametric solution using t and/or s. If there is no solution, enter NONE.)...
3. Consider the following system of linear equations: 2x + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 7z = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working. 2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w....
Find all solutions of the system of equations if possible x,-3y =-6 2x + 6y = 12
determine if the following set of equations has infinitely many solutions or no solutions x-y+2z+w = 4 -2x+3y=-4 x+y+z-4w=3
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...
p x + y+ 2z Subject to x+ 2y + 2z 60 2x +y + 3z 60 +3y+ 6z s 60 Maximize x, y,z 2 0 p x + y+ 2z Subject to x+ 2y + 2z 60 2x +y + 3z 60 +3y+ 6z s 60 Maximize x, y,z 2 0