MATH 3510 Chapter Notes - Chapter 8: Row Echelon Form, Invertible Matrix, Elementary Matrix
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In exercises 5 6, verify that and determine whether the equality holds. In exercises 7 14, use determinants to decide whether the given matrix is invertible. In exercises 15 18, find the values of k for which a is invertible. In exercises 19 23, decide whether the given matrix is invertible, and if so, use the adjoint method to find its inverse. In exercises 24 29, solve by cramer"s rule, where it applies. Cramer"s rule does not apply: show that the matrix is invertible for all values of ; then find using theorem 2. 3. 6, use cramer"s rule to solve for y without solving for the unknowns x, z, and w. , the solution x has integer entries: let. Answer: (a) 189 (b) (c) (d: prove that a square matrix a is invertible if and only if is invertible, show that if a is a square matrix, then.
