In Exercises 13 – 18, use condition (5) to determine whether the given matrix Q is orthogonal.
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Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
- In Exercises 11–16, compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.arrow_forwardFind the inverses of the matrices in Exercises 1–4.arrow_forwardIn Exercises 8–19, calculate the determinant of the given matrix. Use Theorem 3 to state whether the matrix is singular or nonsingulararrow_forward
- In Exercises 19–22, evaluate the (4X4) determinants. Theorems 6–8 can be used to simplify the calculations.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_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 5–8, determine if the columns of the matrix form a linearly independent set. Justify each answer.arrow_forwardFind the general solutions of the systems whose augmented matrices are given in Exercises 7–14.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
- In Exercises 19–20, solve the matrix equation for X. 1 -1 1 -1 5 7 8. 19. 2 3 0| X = 4 -3 1 1 3 5 -7 2 1 -arrow_forwardFind the determinants in Exercises 5–10 by row reduction to echelon form.arrow_forwardEach equation in Exercises 1–4 illustrates a property of determinants. State the property.arrow_forward
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