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In Exercises 1–8, write the augmented matrix for each system of linear equations.
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- In Exercises 15–16, solve each system using matrices. 15. (2x + y = 6 13x – 2y = 16 x - 4y + 4z = -1 2х — у + 52 16. -x + 3y - z =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_forwardUse Cramer’s rule to compute the solutions of the systems in Exercises 1–6.arrow_forward
- In Exercises 1–4, determine if the system has a nontrivial solution. Try to use as few row operations as possible.arrow_forwardIn 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_forwardIn Exercises 7–10, the augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate row operations and describe the solution set of the original system. 1 7 3 -4 1 -4 1 -1 3 7. 8. 1 7 1 1 -2 0 -4 0 -7 1 -1 1 -3 9. 1 -3 -1 4arrow_forward
- Determine which of the matrices in Exercises 1–6 are symmetric. 3.arrow_forwardWrite the augmented matrix as a system of equations 5 1 -3 200 4 1 -3 400 -1 0 1 300 Y + ||arrow_forwardConvert the augmented matrix 4 -1 -4 888 = -1 -4 5 0 -2 to the equivalent linear system. Use x1 and x2 to enter the variables ₁ and ₂.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,