In Problems 35–46 find the general solution of the given system.
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- Problems 74–77 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. 74. To graph g(x) = |x + 2| – 3, shift the graph of f(x) = \x| units 76. Solve: logs (x + 3) = 2 units and then 77. Solve the given system using matrices. number Teft/right| number up/down Зх + у + 2z %3 1 75. Find the rectangular coordinates of the point whose polar 2x – 2y + 5z = 5 x + 3y + 2z = -9 coordinates are ( 6, 3arrow_forward1.2 Find the general solution of dy -2x6 dr +y = y-4arrow_forward5. Find the general solution of the given system. X' = [; x. Х.arrow_forward
- 8. Use any method to find the general solution of the system x + 2 [1/₂].arrow_forward5. The following sets of simultaneous equations may or may not be solvable by the Gaussian Elimination method. For each case, explain why. If solvable, solve. (a) (b) (c) (d) x+y+3z=5 2x + 2y + 2z = 14 3x + 3y+9z = 15 2 -1 1] 4 1 3 2 12 3 2 3 16 2x-y+z=0 x + 3y + 2z=0 3x + 2y + 3z == 0 x₁ + x₂ + x3-X₂ = 2 x1-x₂-x₂ + x₁ = 0 2x₁ + x₂-x3 + 2x4 = 9 3x₁ + x₂ + 2x3-X4 = 7arrow_forward1. Y = 5x + 2 2. 5y = 25x + 10 %3D 3. 5y = 10x + 10 4. 2y = 10x – 4 Which pair of equations forms a system that has infinitely many solutions? 2 and 4 2 and 3 O 1 and 2 O 1 and 4arrow_forward
- Problem 2. i = -x + y – x²? – y² + xy? ý = -y + xy – y² – x²y (1) (2) Determine the values of a for which V (x, y) = x² +ay? is a Lyapunov function for the system.arrow_forwardFind the real-valued general solution to the following systems of equations 2 -5 x'(t) = ({arrow_forward1 -5 2 Let A = 4 -20 12 8 Describe all solutions of Ax = 0. %3D x = 22 +13 +14 3.arrow_forward
- QUESTION 1 Use Gaussian elimination with partial pivoting and three-digit rounding to solve the linear system 3.12xy +1.35z = -120, -4.15x+1.01y +z = 100, x+y+z=125. Then x+y-z= a. -69.6 b. 74 C. -71.5 d. -72.5 e. -70.5arrow_forwardIf the given solutions 2 – 2t yi(t): y2(t) = 2t form a fundamental set (i.e., linearly independent set) of solutions for the initial value problem 21-2 1– 21-1 + 21-2 -23 y, y(3) = t > 0, y -2t-2 2t-1 – 21-2 -34 impose the given initial condition and find the unique solution to the initial value problem for t > 0. If the given solutions do not form a fundamental set, enter NONE in all of the answer blanks. 2t 0) = At) = ( + ( 2tarrow_forwardQuestion 5. Score: 0/1 If the system 6x 2x 14x + 5z 8y 6z = 28y + hz = 4y + = has infinitely many solutions, then k = ४ 4 8 k OF and h =arrow_forward
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