In Exercise 17–36, use the Gauss-Jordan elimination method to find all solutions of the system of linear equations.
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- Find the LU factorization of A = A = -12 -11 X1 = x2 = and use FORWARD SUBSTITUTION AND BACKWARD SUBSTITUTION to solve the system -3 -2 -2 3 3 -2 x3 = 6 X1 x2 -3 x3 ය 3 -2 -2 3 -2 -12 -11 6 9 -14 53arrow_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_forward4. 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_forward
- 2. 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_forwarduse Cramer's Rule to solve the given linear system 2x -y = 5 x + 3y = -1arrow_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
- Find 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 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_forwardSolve the systems of linear equations over the indicated Zp x + 2y = 1 x + y = 2 over Z3arrow_forward
- Find two linearly independent solutions of y" + 1xy = 0 of the form Y1 1+ azx³ + a6x® + · ... Y2 = x + b4x4 + b7x + . ... Enter the first few coefficients: Az = -5/6 help (numbers) a6 help (numbers) b4 help (numbers) b7 help (numbers) I| ||arrow_forward1. Find a basis for the solution space of the system 3x1 X2 + x4 = 0 X1 + x2 + X3 + X4 =0.arrow_forwardUse Cramer's rule to solve the linear system of equations; 2x2 + 5x3 = 1 2x₁ + x₂ + x3 = 1 3x₁ + x₂ = 2arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning