Homework Answers
(c) Consider the system of linear equations 3 1 4a -1x2, where a 2 a a+1 Determine the value(s) o...
(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 =...
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
3. Consider the following system of linear equations: 2x + 2y + 2kz = 2 kx...
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....
1. Consider the following augmented matrix of a system of linear equations: [1 1 -2 2...
1. Consider the following augmented matrix of a system of linear equations: [1 1 -2 2 3 1 2 -2 2 3 0 0 1 -1 3 . The system has 0 0 -1 2 -3 a) a unique solution b) no solutions c) infinitely many solutions with one free variable d) infinitely many solutions with two variables e) infinitely many solutions with three variables
2. In each of the following, find conditions on a, b, and c (if any) such...
2. In each of the following, find conditions on a, b, and c (if any) such that the system has (i) no solution, (ii) a unique solution, and (iii) infinitely many solutions. (b) Ix-2y = 4 | 2x +y – z = a 2x +az= 6 2y +3z= b | 3x – 4y + 5z = b IX – cz = 1 [3]
3. Consider the following system of linear equations: 2.0 + 2y + 2kz = 2 kx...
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 +...
Have som problem solving this problems in MATHEMATICAL METHODS 2. Can someone help me solve and ...
Have som problem solving this problems in MATHEMATICAL METHODS
2.
Can someone help me solve and
explain this problems?
Problem 1. Solve the following systems of linear equations: 4x+3y + z = 9 3x+y-z = 3 x4 Problem 2. Find the values of the parameters a and p for which the system x+5y = 6, has: (i) a unique solution, (ii) infinitely many solutions, (iii) no solutions. Hint: Use the following fact: a system with as many unknowns as equations...
The reduced row echelon form of a system of linear equations in x and y or...
The reduced row echelon form of a system of linear equations in x and y or in x, y and z is given. For each system, determine whether it has a unique solution (in this case, find the solution), infinitely many solutions, or no solutions. 1. [ 1 0 I 0 ] [ 0 1 I 0 ] [ 0 0 I 0 ] A. No solutions B. Infinitely many solutions C. Unique solution: x=1,y=1,z=0 D. Unique solution:...
Using Mathematica: (2x – 3y = 4 4. Consider the system of equations: 1-2 +1.5y =...
Using Mathematica:
(2x – 3y = 4 4. Consider the system of equations: 1-2 +1.5y = 3 (a) Graph the two lines corresponding to this system, and use the graph to decide if the system has a unique solution, no solution or infinitely many solutions. (b) Solve the system using Mathematica, and check if the answer matches your answer from part (a).
4. Consider the linear system /1 2 T2 -2 1 2 1 3 22-3) 4 :)...
4. Consider the linear system /1 2 T2 -2 1 2 1 3 22-3) 4 :) [4] (a) Determine the value(s) of a, if any, for which this system has precisely one solution [2] (b) Determine the value(s) of a, if any, for which this system has no solutions [2] (c) Determine the value(s) of a, if any, for which this system has infinitely many solutions
(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
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....
1. Consider the following augmented matrix of a system of linear equations: [1 1 -2 2 3 1 2 -2 2 3 0 0 1 -1 3 . The system has 0 0 -1 2 -3 a) a unique solution b) no solutions c) infinitely many solutions with one free variable d) infinitely many solutions with two variables e) infinitely many solutions with three variables
2. In each of the following, find conditions on a, b, and c (if any) such that the system has (i) no solution, (ii) a unique solution, and (iii) infinitely many solutions. (b) Ix-2y = 4 | 2x +y – z = a 2x +az= 6 2y +3z= b | 3x – 4y + 5z = b IX – cz = 1 [3]
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 +...
Have som problem solving this problems in MATHEMATICAL METHODS
2.
Can someone help me solve and
explain this problems?
Problem 1. Solve the following systems of linear equations: 4x+3y + z = 9 3x+y-z = 3 x4 Problem 2. Find the values of the parameters a and p for which the system x+5y = 6, has: (i) a unique solution, (ii) infinitely many solutions, (iii) no solutions. Hint: Use the following fact: a system with as many unknowns as equations...
Using Mathematica:
(2x – 3y = 4 4. Consider the system of equations: 1-2 +1.5y = 3 (a) Graph the two lines corresponding to this system, and use the graph to decide if the system has a unique solution, no solution or infinitely many solutions. (b) Solve the system using Mathematica, and check if the answer matches your answer from part (a).
4. Consider the linear system /1 2 T2 -2 1 2 1 3 22-3) 4 :) [4] (a) Determine the value(s) of a, if any, for which this system has precisely one solution [2] (b) Determine the value(s) of a, if any, for which this system has no solutions [2] (c) Determine the value(s) of a, if any, for which this system has infinitely many solutions
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