In Exercises 21–23, use determinants to find out if the matrix is invertible.
23.
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- In Exercises 27–32, evaluate the determinant of the given matrix by inspection.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_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
- Compute 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_forwardUse Cramer’s rule to compute the solutions of the systems in Exercises 1–6.arrow_forwardFind the determinants in Exercises 5–10 by row reduction to echelon form. just number 7arrow_forward
- Compute 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_forwardDetermine which of the matrices in Exercises 1–6 are symmetric. 3.arrow_forwardFind the determinants in Exercises 5–10 by row reduction to echelon form.arrow_forward
- Evaluate 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_forwardIn Exercises 8–19, calculate the determinant of the given matrix. Use Theorem 3 to state whether the matrix is singular or nonsingulararrow_forwardEach equation in Exercises 1–4 illustrates a property of determinants. State the property.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage