In Exercises 1 – 12, determine whether the given matrix A is diagonalizable. If A is diagonalizable, calculate
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
- In Exercises 5β8, use the definition of to write the matrix equation as a vector equation, or vice versa.arrow_forwardIn Exercises 11β16, compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.arrow_forwardUnless otherwise specified, assume that all matrices in these exercises are nxn. Determine which of the matrices inΒ Exercises 1β10 are invertible. Use as few calculations as possible. Justify your answersarrow_forward
- In Exercises 29β32, 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 13β18, 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 γγ 2. 1. 2. 1. 3.arrow_forwardIn Exercises 19β20, 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_forward
- In Exercises 19β22, evaluate the (4X4) determinants. Theorems 6β8 can be used to simplify the calculations.arrow_forwardFind the determinants in Exercises 5β10 by row reduction to echelon form.arrow_forwardSolve each system in Exercises 1β4 by using elementary rowoperations on the equations or on the augmented matrix. Followthe systematic elimination procedure described in this section.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning