Consider the following system of linear equations: 2 2x + + 3y - 22 7y -...
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....
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.
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).
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given (0) 3 and y(0)-4 (d) Verify the calculations with MATLAB Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the...
3. Write the following systems of linear equations using augmented matrix form a. 6x+7y= -9 X-y= 5 b. 2x-5y= 4 4x+3y= 5 C. x+y+z= 4 2x-y-z= 2 -x+2y+3z= 5 4. Solve the following Systems of linear equations using Cramer's Rule a. 6x-3y=-3 8x-4y= -4 b. 2x-5y= -4 4x+3y= 5 c. 2x-3y+z= 5 X+2y+z= -3 x-3y+2z= 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 +...
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)
Use the Gauss-Jordan method to solve the following system of equations. 5x+4y-3z+0 2x-y+5z=1 7x+3y+2z=1 Multiple Choice A.The solution is B.There is an infinite number of solutions. The solution is C. There is no solution.
+ 3y - 5z = bi Consider the linear system of equations: 3 + 4y - 8z = 62 -I - 2y + 2z = b3 (a) Show that A is not onto. (b) Using R.R.E.F., find a solvability condition on (b1,b2, 63) which guarantees a solution Adjoint Theorem. (c) Reproduce your solvability condition in (b) using the adjoint theorem.
Solve the following linear systems of equations by Gaussian elimination. 3x+3z=0 2x+2y=2 3y+3z=3