In Exercise 17–36, use the Gauss-Jordan elimination method to find all solutions of the system of linear equations.
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- 5. By using the matrix methods to solve the following linear system: I1 + 12 – 13 = 5, 3r1 +x2 – 2r3 = -4, -I1 + 12 - 2r3 = 3;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_forward1. Find a basis for the solution space of the system 3x1 X2 + x4 = 0 X1 + x2 + X3 + X4 =0.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_forwardPlease show solutionarrow_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_forward
- a) Find the matrix of the quadratic form. Assume x is in R3 5xỉ-x} +7x3-5x1X2 -3x1X3arrow_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_forwardWrite the following matrix equation form into a system of linear equationsarrow_forward
- Let 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_forwardConsider the matrix A - A. Verify that the matrix B I. = 2 = -1 -3 1 1 B. Use this fact to solve the following system of linear equations. 2x1 3x₂ + x3 x1 + x₂ - X3 -x₁ + x₂ − 3x3 = 0 1 -1 -3 1/7] 4/7 -2/7 5/14 -1/7 -1/14 -5/14_ 2, : -1, -1/7 -3/14 is the inverse of matrix A.arrow_forwardUse an LU-factorization of the coefficient matrix to solve the follow- ing system of linear equations. x + 2y + z = 1 x + 2y – z 3 x – 2y + z -3.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage