In Problems 1–12 find the general solution of the given system.
3.
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- 8. Use any method to find the general solution of the system x + 2 [1/₂].arrow_forwardWhich of the following is a solution to the given system of equations found below? (1) x = – /Y %3D (2) y? – x² = 6 O (-v2, 2) O (3, V3) O (-v2, –2) O (-v3, 3)arrow_forward2. (10 points) Find the general solution of the following first order system. x = 5x1 – 6x2 + 3e² x2 = 3x1 – 4.x2 + et %3D -arrow_forward
- 1. For which values of k will the following system have no solution? Exactly one solution? Infinitely many solutions? x + ky - 2z = 0 x + 2ky – 2z = 5 x + ky + (k^2 –- 3k)z = k – 1arrow_forwardProblem 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_forwardQ.1. Explain why the linear system has no solution: 1 0 3 1 0 1 2 4 0 0 0 For which values ofk does the system below have a solution? x-3y = 6 + 3z = -3 2x + ky + (3 – k)z = 1arrow_forward
- Given the matrix, A 2 -1 3 find A-1, using the Gauss-Jordan method 1 8 Solve the following system of equationsarrow_forward[1 1 1] 024. The system of equations | 0 0 1x=| b, | is solvable if |0 0 1 b, (c) b, = b, (d) b, = 0 (e) none (a) h, = b, = 0 (b) b, = b, # 0 025. If A = B+C and B= B' and C' =-C, then %3D %3D (1) C = A– A" »C=÷(4- A') (6) C=;(4+A") (4) C = A+ A" (e) none c=-(4-A') (0) C = (A+ A°) («)C= A+ A°arrow_forward> Moving to another question will save this response. Question 4 1-3 The solution of the system x': = - (2-2)x is a. 0+ 2 O b. ²( ³ ) e ² + c ² ( 1 ) e ²t 2t 3 X=C1 2 -2t ² ( ²³ ) e − ² + c ₂ ( 1 ) e - ²² 3 X=C1 Oc. none of the above O d. 3 1 -t =( ² ) e - ² + c ₂( ² ) 0 C2 le 2 1 "X=C1₁| -2t 3 2t 0*x+²²(²) *² + √( 1 ) ²² Oe. Ox=C1 2 A Moving to another question will save this response.arrow_forward
- 4. For which values of a will the following system have (a): no solution, (b): Unique solution, (c): Infinitely many solutions? x + 2y- 3z = 4 3x y+ 5z = 2 - 4x + y+(a² – 14)z = a + 2arrow_forward3. Find the general solution of the system given by Y2 + Y3 Y2 = Yı + Y3 (3) Yı + Y2 || || ||arrow_forward2. How many solutions could the following linear system have? ax+by=0 cx + dy=0 ex+fy=0 Give an example of such a system for each possibility.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning