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Consider the following system of linear equation x+2y +z = 0 x+y-z=-1 2x-y+z=4 Which of the...
Consider the following system of linear equation x+23 + 0 x+y=z= -1 2x - 4 Which of the following ordered Gaussian operations can be considered for finding the value ofz? 1. (-2R+ RyR; || - R+R R -R + R, R} II. -2R, + R— R1-2, +R, R-6R + Rx-R R R II.-R,+R R 1|-2R, + Ry → R || -3R + RR) IV. -2R, + Rs — R, ||-R+RR. || -3R, +R, R R, R} v. ( - R+R,...
b) Consider the system of simultaneous equations for x,y and z: ( x + 2y + z = 3 r-3y+z=1 (2x - y +2 = 4 Use Gaussian elimination to find if these equations are consistent. Pro- vide a geometrie interpretation of the result. (18 marks) [Total 35 marks)
1. Given y” + 3y' - 2y 0. Give the characteristic equation (the quadratic equation that finds the roots). (a) r2+ 3r - 2 = 0 (b) r2+ 3r + 2 = 0 (c) 2r2+ 3r - 1 = 0 (d) 2r2+ 3r + 1 = 0 (e) r2+r-2 = 0 (f) r2+r+ 2 = 0 (g) 2r2 +r-1=0 (h) 2r2+r+ 1 = 0 2. Find the larger root of the auxiliary equation of the differential equation y” + 3y...
Solve 3x + 2y – z = 1x – 2y + z = 02x + y – 3z = -1
Which of the following are linear transformations? f: R3 R2 [x, y, z] [7x - 2y, 0 h R R x > sin x g R2R [x, y] [y- x, 2 the map T R > R< described by reflection in a line L: 2x + 7y = 0 through the origin.
Use Gaussian Elimination only to solve 3x - 2y + z = 13 -2x + y + 4z = 11 x + 4y - 5z = -31
Consider the following system of linear equations. 5x -=-31 - 2x - 2y +z = 17 --5y +2z = 7 Solve the system by completing the steps below to produce a reduced row-echelon form. R1, R2, and Rz denote the first, second, and third rows, respectively. The arrow notation (-) stands for "replaces," where the expression on the left of the arrow replaces the expression on the right. 08 5 0 -1-31 ? Here is the augmented matrix: -2 -2...
Solve using Cramer's Rule X – 2y +z=7 2x +y – z=0 3x + 2y – 2z = -2 O (1,-2,0) O (2,-1,3) O (1,-1,1) No Solution
1 (a) Employ the method of Gaussian elimination to solve the system of linear equations x+2y + 22= 4, 2x + y- z=-1 (b) State Cramer's rule for the solution of systems of linear equations, and use it to calculate the solution of the system of equations in (a)
4. Find the complete solution to the system 2y z t = 1 2x - y - z -t = 3 3x 2z - 2t = -2