In Exercises 11–16, compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.
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- In Exercises 27–32, evaluate the determinant of the given matrix by inspection.arrow_forwardUse Cramer’s rule to compute the solutions of the systems in Exercises 1–6.arrow_forwardIn Exercises 11–16, compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.arrow_forward
- In Exercises 5–8, use the definition of to write the matrix equation as a vector equation, or vice versa.arrow_forwardIn 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_forwardUnless otherwise specified, assume that all matrices in these exercises are nxn. Determine which of the matrices in Exercises 1–10 are invertible. Use as few calculations as possible. Justify your answersarrow_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_forward4 11. 5 3 2 -2 2arrow_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_forward
- Find the determinants in Exercises 5–10 by row reduction to echelon form. just number 7arrow_forwardIn Exercises 8–19, calculate the determinant of the given matrix. Use Theorem 3 to state whether the matrix is singular or nonsingulararrow_forwardFind the general solutions of the systems whose augmented matrices are given in Exercises 7–14.arrow_forward
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