In Exercises 1 –6, solve the system Ax = b using the given LU factorization of A.
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Linear Algebra: A Modern Introduction
- In Exercises 27–32, evaluate the determinant of the given matrix by inspection.arrow_forwardSolve each system in Exercises 1–4 by using elementary rowoperations on the equations or on the augmented matrix. Followthe systematic elimination procedure described in this section.arrow_forwardIn Exercises 5–8, use the definition of Ax to write the matrix equation as a vector equation, or vice versa. 5. 5 1 8 4 -2 -7 3 −5 5 -1 3 -2 = -8 - [18] 16arrow_forward
- In Exercises 7–10, determine the values of the parameter s for which the system has a unique solution, and describe the solution.arrow_forwardFind the determinants in Exercises 5–10 by row reduction to echelon form.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
- Find the determinants in Exercises 5–10 by row reduction to echelon form. just number 7arrow_forwardIn Exercises 8–19, calculate the determinant of the given matrix. Use Theorem 3 to state whether the matrix is singular or nonsingulararrow_forward1. Suppose that (1,5, 1,4) and (2, 1,7, 2) are two solutions of the system Ax = b. Find three distinct non-trivial solutions of Ax = 0. %3D Hint: Use the linear properties of the product Ax from section 1.4.arrow_forward
- In Exercises 29–32, find the elementary row operation that trans- forms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first.arrow_forward[M] In Exercises 37–40, determine if the columns of the matrix span R4.arrow_forwardIn Exercises 5–8, determine if the columns of the matrix form a linearly independent set. Justify each answer.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage