In Problems 35– 46 find the general solution of the given system.
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- 4. Use Gaussian elimination with backward substitution to solve the following linear system: 2x1 + x2 – x3 = 5, x1 + x2 – 3x3 = -9, -x1 + x2 + 2x3 = 9;arrow_forwardQuestion 5. Determine all solutions to the first-order linear system x₁ = −x1 + x2 x = -2x1-3x2 + 23 - x = x1 + x2 − 2x3arrow_forwardH.W:- Solve The linear SysTem O 1.7X-3.2y = 81 014x+112y = -2 2X+X2- X3=D9 8 X2+ 6X3=-6 -2 X1+4x2-6X3= Y0 %3D ®2x+3y+2-1/W = | 5x -2y+5z-4w=S X-Y+32-3w=3 3ペナ9yーチスナ2w=ー7arrow_forward
- 5. How many solutions does the system y = 3x? and y = 7x + 6 have? [A] 1 (B] 2 [C13 [D]4arrow_forward6. How many solutions does the system 2y = 10x – 14 and 5x – y = 7 have? C none A one B two D infinitely manyarrow_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
- 3. Find the general solution of the system given by Y2 + Y3 Y2 = Yı + Y3 (3) Yı + Y2 || || ||arrow_forward4. 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_forward35. Solve the following system of nonlinear equations for x, y, and z. x² + y? + z = 6 x² - y? + 2z = 2 2r + y - = 3arrow_forward
- 8. Use any method to find the general solution of the system x + 2 [1/₂].arrow_forwardProblem. 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_forward51. Suppose that -1 -2 -i A and D = -5 Find X such that AX = D by %3D (a) solving the associated system of linear equations and (b) using the inverse of A.arrow_forward
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