Question 8 [2] Determine whether or not the planes with equations -2x + 2y + 3z...
Solve the following linear systems of equations by Gaussian elimination. 3x+3z=0 2x+2y=2 3y+3z=3
2. Consider the planes PCR and P2 CR3 defined respectively by the equations 2x - y - 32 = 0 and x - 2y + 2 = 0. P = { u= ER", such that 2x - y - 32 = 0 ---0-- --40) - P2 = = ER", such that - 2y + 2 = 0 (a) (6 points) Construct a basis for P. and P2 (b) (2 points) Why the subset Pin P, is a subspace of R3
10. Let E be the tetrahedron bounded by the planes 2x +2y +2=6,1 = 0, y = 0, and 2 = 0. Express the following integral as an iterated double integral. Do not evaluate. SIS 6.ry dy
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 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...
UWVG 2020 13 of 18 (8 complete) Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 7x + 16y + 2z = 20 3x + 7y + 3z = -8 X+ 2y - 4z = 5 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. There is one solution. The solution set is {(C 1 0 ). (Simplify your answers.)...
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 +...
of Equations There are generally two approaches to solving systems of equations in physics, the substitution method and the addition method. Let us consider the system of two equations below: 4x + 2y 14 2x -y-1 We can solve these equations using both methods. First, the substitution method. The process is as follows: In one of the equations, solve for one of the variables . te this expression for that variable into the other equation. This will leave an expression...
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...
Please explain your solution wherever possible, thank you! PROBLEM 3 Determine whether each of the differential equations is exact. If it is exact, find the solution (2 +3)(2y - 2)y0. PROBLEM 3 Determine whether each of the differential equations is exact. If it is exact, find the solution (2 +3)(2y - 2)y0.