In Exercise 17–36, use the Gauss-Jordan elimination method to find all solutions of the system of linear equations.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Finite Mathematics & Its Applications (12th Edition)
- 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_forward6. Use Cramer’s Rule to solve for x3 of the linear system 2x1 + x2 + x3 = 63x1 + 2x2 − 2x3 = −2x1 + x2 + 2x3 = −4arrow_forwardFind 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_forward
- In Exercises 1 through 12, find all solutions of the equations with paper and pencil using Gauss–Jordan elimination. Show all your work.arrow_forwardClassify the quadratic forms in Exercises 9–18. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct P using the methods of Section 7.1. 11. 2x² + 10x1x2 + 2x3arrow_forwardIn Exercises 5–8, use the definition of to write the matrix equation as a vector equation, or vice versa.arrow_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_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_forwardConsider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?arrow_forward
- Find a matrix X = R2x2 for which −3 X¹⁹ - -24 12² -36).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_forwardLet a and b be integers.(a) Show that b is a linear combination of a + 3b and a + 2b.(b) Show that a is a linear combination of a + 3b and a + 2b.(c) Conclude that if (a, b) is not equal to (0, 0) then gcd(a, b) = gcd(a + 3b, a + 2b).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning