In Problems 35–46 find the general solution of the given system.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- Problem. Compute the general solution of the following 3 x 3 linear system: -2 3 0 dY *- (1 ÷ 9x ---- () = 3 -2 1 Y, where . dt 0 0 -1 (Hint: Mimic the computation of the general solution of a 2 x 2 linear system!)arrow_forwardFind the general solution of the system of D.E. x ¹ 1 (11) 4 १४arrow_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
- 1.3.1 Use elementary operations to solve the system of equations 3x + y = 3 x + 2y = 1.arrow_forward1. Write the solution of the linear system -x1 – 14 + 2.x5 = -2 3x1 + x2 + 2x3 + 4x4 – x5 1 4.x1 – x2 + x3 + 2x5 1 in the form x Xp + Th where x, is a particular solution and rh is a solution of the corresponding homogeneous system.arrow_forward3. Find the general solution of the system given by Y2 + Y3 Y2 = Yı + Y3 (3) Yı + Y2 || || ||arrow_forward
- 10. For which values of the parameter a does the following linear system have (i) a unique solution, (ii) no solution? 2x3y = 0 x + ay = 1arrow_forwardIn Problems 19–56, solve each system of equations. If the system has no solution, say that it is inconsistent. For Problems 19–30, graphthe lines of the systemarrow_forward7. Find the general solution of the system: X = ( 2 -1 3 X+ et ()+arrow_forward
- Which 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_forward1. Solve the following system using either Gaussian elimination or Gauss-Jordan elimination. x- y- 3z = 7 f 3x +2y – z = 8 4x + y+ z = 10arrow_forward2. Given the following 2 x 2 linear system with constant coefficients x' = Ax (H) x= Ax+g(t), (N) where g is not the zero vector. Which of the following statements are true? Justify your answers. A. If , is a solution to (H) and 7, is a solution to (N), then , +27, is a solution to (N). B. If , and 2 are both solutions to (N), then ₁-2 is a solution to (H).arrow_forward
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