Question 1 (8 marks) Consider the linear system x - 2y + 2z = -1 -2x...
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 2x + 2y + 2z = 4 2y + 2z = 2 3y + 32 = 3 (1, 1.01 (1.1.) (1,1-t. ) The system has no solution. 11.0.1)
3. Consider the following system of linear equations: 2.0 + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 72 = 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. 4. Solve the following system of linear equations using Gauss-Jordan elimination: x1 + x2 - 2.13 + 24 +3.25 = 1 2.x1 - x2 +...
(c) Consider the system of linear equations 3 1 4a -1x2, where a 2 a a+1 Determine the value(s) of a such that the system is is a scalar. (i) consistent with infinitely many solutions; (ii) consistent with one and only one solution; and (ii) inconsistent. 20 marks Solve the system when it is consistent. (c) Consider the system of linear equations 3 1 4a -1x2, where a 2 a a+1 Determine the value(s) of a such that the system...
1-1 11?? (c) Consider the system of linear equations | 3 1 40-1 | x = | 2 | , where a 2 a a+1 is a scalar. (i) 1 (ii) Determine the value(s) of a such that the system is consistent with infinitely many solutions; consistent with one and only one solution; and , (iii) inconsistent. Solve the system when it is consistent. 20 marks
Consider the following system of linear equations: 2 2x + + 3y - 22 7y - 3z ky + 5z = = = 2 6 5 Find the value of k so that the system has no solutions. Your value of k should be an integer. Answer: Check
Given a system of linear equations: w + 2x - 3y + 4z = 1 3w + 6x - 9y + tz = 2 (i) Express the system in [A][b] form.(ii) Determine the value of t such that: - the system is consistent; and - the system is inconsistent. (iii) Determine the rank of A, and by using the Rank Theorem, determine the number of free variables.
1 (8+7 15 pts) Linear equations Consider the system of equations 1 -1 0 0 0 0 1 2-1 03 - 0 0 1 2 3 4 4 (a) Determine all values of a and b such that this system is 1 inconsistent (ii) consistent (b) Find the set of solutions for 1 a b 2.
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)
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...