Concept explainers
In Exercises 1–12, use the Gauss–Jordan method to compute the inverse, if it exists, of the matrix.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Finite Mathematics & Its Applications (12th Edition)
- In Exercises 19–20, solve the matrix equation for X. 1 -1 1 -1 5 7 8. 19. 2 3 0| X = 4 -3 1 1 3 5 -7 2 1 -arrow_forwardUnless otherwise specified, assume that all matrices in these exercises are nxn. Determine which of the matrices in Exercises 1–10 are invertible. Use as few calculations as possible. Justify your answersarrow_forwardDetermine which of the matrices in Exercises 1–6 are symmetric. 3.arrow_forward
- In Exercises 19–22, evaluate the (4X4) determinants. Theorems 6–8 can be used to simplify the calculations.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_forwardUse Cramer’s rule to compute the solutions of the systems in Exercises 1–6.arrow_forward
- 4 11. 5 3 2 -2 2arrow_forwardIn Exercises 13–18, perform each matrix row operation and write the new matrix. -6 4| 10 13. 1 5 -5 3 4 7 -12 6 9 40 3. 14. 1 -4 7|4 2 0 -1 |7 1 3 -3 15. 1 -3R, + R, -2 -1 -9- -9- 16. 3 3 -1 10 -3R + R2 1 3 5 1 -1 1 1 3. 1 -2 -1 17. 2 4| 11 -2R, + R3 5 1 6. -5R, + R4 1 -5 2 -2 4 -3 -1 18. 3 2 -1 -3R + R3 -4 4 2-3 4R, + R4 -len すす 2. 1. 2. 1. 3.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 5–8, use the definition of to write the matrix equation as a vector equation, or vice versa.arrow_forwardFind the general solutions of the systems whose augmented matrices are given in Exercises 7–14.arrow_forwardEach equation in Exercises 1–4 illustrates a property of determinants. State the property.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning