Find the determinants in Exercises 5–10 by row reduction to echelon form.
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Chapter 3 Solutions
Linear Algebra and Its Applications (5th Edition)
- In Exercises 41–42, evaluate each determinant. 3 1 7 -1 14 -3 7 -5 |-2 1 5 41. 42. 19 -6 4 1 0 7 3 5| 4 -3 5 6.arrow_forwardFind the determinants in Exercises 5–10 by row reduction to echelon form.arrow_forwardClassify the quadratic forms in Exercises 9–18. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct P using the methods of Section 7.1. 11. 2x² + 10x1x2 + 2x3arrow_forward
- Compute 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_forwardIn Exercises 27–32, evaluate the determinant of the given matrix by inspection.arrow_forwardCompute the determinants in Exercises 1–8 using a cofactor expansion across the first row. In Exercises 1–4, also compute the determinant by a cofactor expansion down the second column. just number 5arrow_forward
- In Exercises 35–42, find all real values of x for which fx0. f(x)=x3−x2−3x+3arrow_forwardEvaluate each determinant in Exercises 1-10. 1. 5 7 2. 4 5 6 8 3 3. -4 1 4. 7 9. 6. -2 -5 5. -7 14 1 3 -4 -8 2 7. -5 8. -2 9. 10. 2 6. 2. 2. -IN-10arrow_forwardCompute the determinants in Exercises 1–8 using a cofactor expansion across the first row. In Exercises 1–4, also compute the determinant by a cofactor expansion down the second column.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning