In Exercises 1 – 14, find the characteristic polynomial and the eigenvalues for the given matrix. Also, give the algebraic multiplicity of each eigenvalue. [Note: In each case the eigenvalues are integers.]
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Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
- Compute the determinants in Exercises 9β14 by cofactor expansions. At each step, choose a row or column that involves the least amount of computation.arrow_forwardIn 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 27β32, evaluate the determinant of the given matrix by inspection.arrow_forward
- In Exercises 5β8, use the definition of to write the matrix equation as a vector equation, or vice versa.arrow_forwardIn Exercises 19β22, evaluate the (4X4) determinants. Theorems 6β8 can be used to simplify the calculations.arrow_forwardEach equation in Exercises 1β4 illustrates a property of determinants. State the property.arrow_forward
- In Exercises 11β16, compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.arrow_forwardFind the determinants in Exercises 5β10 by row reduction to echelon form. just number 7arrow_forwardCompute the determinants in Exercises 1β8 using a cofactor expansion across the first row. In Exercises 1β4, also compute the determinant by a cofactor expansion down the second column.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage