In Exercises 1–12, use the Gauss–Jordan method to compute the inverse, if it exists, of the matrix.
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Finite Mathematics & Its Applications (12th Edition)
- Determine which of the matrices in Exercises 1–6 are symmetric. 3.arrow_forwardIn Exercises 19–22, evaluate the (4X4) determinants. Theorems 6–8 can be used to simplify the calculations.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 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 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_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_forward
- Find the general solutions of the systems whose augmented matrices are given in Exercises 7–14.arrow_forward[M] In Exercises 37–40, determine if the columns of the matrix span R4.arrow_forwardCompute the determinants in Exercises 9–14 by cofactor expansions. At each step, choose a row or column that involves the least amount of computation.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage