In Exercise 17–36, use the Gauss-Jordan elimination method to find all solutions of the system of linear equations.
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Finite Mathematics & Its Applications (12th Edition)
- 3. Solve the linear system of equations x1 – *2 + 2x3 - -2, -201 +x2 – 03 – 2, 4x1 – x2 + 203 – 1, using 3 digit rounding arithmetic and Gaussian elimination with partial pivoting.arrow_forwardConsider the system of equations 2a + 36 – c = 5 -a + b+c= 4 5a – 26 + 3c = 10 - (a) Solve it in numbered steps by Gauss-Jordan elimination. (b) Write out the problem in matrix notation Ax = b. Now write out the S, R, or P matrix corresponding to each of your step in (a).arrow_forwardIn Exercises 13–17, determine conditions on the bi ’s, if any, in order to guarantee that the linear system is consistent. 13. x1 +3x2 =b1 −2x1 + x2 =b2 15. x1 −2x2 +5x3 =b1 4x1 −5x2 +8x3 =b2 −3x1 +3x2 −3x3 =b3 14. 6x1 −4x2 =b1 3x1 −2x2 =b2 16. x1 −2x2 − x3 =b1 −4x1 +5x2 +2x3 =b2 −4x1 +7x2 +4x3 =b3 17. x1 − x2 +3x3 +2x4 =b1 −2x1 + x2 + 5x3 + x4 = b2 −3x1 +2x2 +2x3 − x4 =b3 4x1 −3x2 + x3 +3x4 =b4arrow_forward
- 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_forwardPlease show your work for all questions. Thank you in advance!arrow_forward2. Use Gauss elimination with back substitution to solve the system of linear equations: &x, +x2 +4x3 +8x, = 5 x1 - 7x, – 2x, – 7x4 : 1 7x, - 2x2 + 7x3 +2x4 =-5 X1 +x, +2x3 – 6x, = -5 Round-off to 5 significant figures.arrow_forward
- Consider the difference equation an+2+an+1+an = 0. (a) Write down the associated discrete linear system n+1 = An- (b) Find a formula for A" and use this to give an explicit expression for an in terms of ao and a₁. [Hint: Note that A" has only 3 values.]arrow_forwardUse Cramer's rule to solve the linear system of equations; 2x2 + 5x3 = 1 2x₁ + x₂ + x3 = 1 3x₁ + x₂ = 2arrow_forwardLet Ax = b be a linear system with real coefficients such that A is an m × n matrixand Ax = b has a unique solution. What can you say about m, n? Explain how to picka subsystem of n equations in Ax = b such that the two systems have the same solutions.arrow_forward
- Use Gaussian Elimination Method to solve this linear system:arrow_forwardFind two linearly independent solutions of y" + 9xy = 0 of the form y₁=1+a3x³ +a6zº +... 32= x+bx+b7x² + ... Enter the first few coefficients: a3 a6 ba b7 || help (numbers) help (numbers) help (numbers) help (numbers)arrow_forwardConsider the following system of linear equations for four real variables x1, x2, x3, X4: X2 + x3 2x4 -3 - Xị + 2x2 – X3 2x1 + 4x2 + x3 – – 3x4 -2 - 1 — 4х2 — 7хз — 24 7x3 -19 - - Write down the augmented matrix (A|b) of this system of linear equations.arrow_forward
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