3.Consider the following system of equations: 2x+3y + z-1 xy4 Write this system of equations in...
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...
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).
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....
Consider the following linear system of differential equations: dx/dt = 2x-3y dy/dt = -x +4y (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 x(0) = 3 and y(0) = 4 (d) Verify the calculations with MATLAB
Consider the linear system in three equations and three unknowns: 1) x + 2y + 3z = 6, 2) 2x − 5y − z = 5, 3) −x + 3y + z = −2 . (a) First, identify the matrix A and the vectors x and vector b such that A vector x = vector b. (b) Write this system of equations as an augmented matrix system. (c) Row reduce this augmented matrix system to show that there is exactly...
Q) Consider the following set of linear equations. ix-iz=i iy-iz=0 ix -iy z-1 a) Write the above system of equations in matrix form. (AX-B) b) Find x, y, z using Gauss elimination method c) Find the determinant of the coefficient matrix A.
solve for x and y, linear equations using the elimination method 2x+6y=-2 5x-3y=3 and -9x+3y=5 9x+4y=-6 is the following system dependentinconsistent or does it have a unique solution? why is this so? x-8y=9 6x-48y=36
Consider the system of equations shown below. 2x - 4y + 5z = 10 -7x + 14y + 4z = -35 3x - 6y + z = 15 (a) Determine whether the nonhomogeneous system Ax = b is consistent. O consistent O inconsistent (b) If the system is consistent, then write the solution in the form x = Xp + xn, where xp is a particular solution of Ax = b and xn is a solution of Ax = 0....
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
UseGauss-Jordan method to solve the following system of linear equations 2x – 3y + z = 0 5x + 4y + z = 10 2x – 2y – z = -1