Find the characteristic polynomial and the eigenvalues of the matrices in Exercises 1–8.
2.
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- 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 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_forward1 -2 1 32. 4 -7 3 -2 6 -4arrow_forward
- In Exercises 5–8, use the definition of to write the matrix equation as a vector equation, or vice versa.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_forwardCompute the determinants in Exercises 1–8 using a cofactor expansion across the first row.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.arrow_forwardIn Exercises 27–32, evaluate the determinant of the given matrix by inspection.arrow_forwardFind the characteristic polynomial of the matrix 1 -2 A = -1 -3 5 3arrow_forward
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