For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7 For 18-2...
1. (a) Express the following system of equations in augmented matrix form. 2x - 4y + 5z = 9 x + 3y + 8z = 41 6x + y - 3z = 25 (2 marks) (6) Use Gaussian elimination to solve the system of equations. (6 marks) 2. Given that a matrix A: 18 A= 1 8 -1 4 -1 -1 -1 8 (a) Determine AT. (6) Calculate the det (A). (2 marks) (6 marks) 3. Refer to the graph...
Problem 1: Given the following function - 4x 4.x2 + 4y2 + 4y +1 1- 4x2 – 4x2 + 4y2 + 4y +1 (a) Show that f is analytic (on its domain of definition); (b) Find a formula for f in terms of variable z (c) Find f'(z).
Solve the system of linear equations and check any solutions
algebraically.
2x + 4y + z = 3 x – 2y 3z = 4 x + y – z = -1
EXAMPLE 1 Find the tangent plane to the elliptic paraboloid z = 2x2 + 4y2 at the point (1, 1, 6). SOLUTION Let f(x, y) = 2x2 + 4y. Then f(x, y) = fy(x, y) = fx(1, 1) = fy(1, 1) = Then this equation gives the equation of the tangent plane at (1, 1,6) as (x + 1) + (y - 1) Z or ZE
1. (a) Express the following system of equations in augmented matrix form. 2x - 4y + 5z = 9 x + 3y + 8z = 41 6x + y - 3z = 25 (2 marks) (b) Use Gaussian elimination to solve the system of equations. (6 marks)
For questions 12-17, match the graph with its equation. If it is a quadratic surface, give the name of the surface +3z2 = 1 12. [2] 2x2 13. [2] y 4x = 14. [2] x2-z2y 15. [2] 2z x2 4y2 16. [2] 2x22-z2 =1 17. [2] z 4y -x F
For questions 12-17, match the graph with its equation. If it is a quadratic surface, give the name of the surface +3z2 = 1 12. [2] 2x2 13. [2] y...
- 2x+4y+ 3Z = -27 xtsy-z = -2 3xty-42=25 Use Gauss-Bordan to solve write answer in format (o (xy, z 1
Problem ONE UseGauss-Jordan method to solve the following system of linear equations 2x - 3y +z = 0 5x + 4y +z = 10 2x - 2y - z= -1 Problem TWO Find the eigenvalues and the corresponding eigenvectors of the matrix [1 0 1 0] 0 1 1 0 0 0 20 LO 0 0 2] Problem THREE Solve the following DE x2y" - 3xy' + 4y = x2 Inx, X>0 Problem FOUR Solve the following DE y (4)...
QUESTION 3 Given the following equations: 2x + 3y + z = 13 3x – 4y + 2z=3 x + y + z = 6 Determine x, y, and z. X = , y = and z =
(1 point) Give a geometric description of the following system of equations 1 2x + 4y - 6z Two parallel planes = " -3- 6y + 9x = 2x + 4y - 62 = Two parallel planes 2. ** –3x - 6y + 9z = 4y - O2 = Two planes intersecting in a line 73. 21 * -x + 5y - 92 = 12 16 –12 18 12 1 T