Page 142 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
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19.

20.

21.

     Show that the matrix
22.

     is invertible for all values of ; then find using Theorem 2.1.2.
     Use Cramer's rule to solve for without solving for , , and .
23.

     Let  be the system in Exercise 23.
24.

(a) Solve by Cramer's rule.

(b) Solve by Gauss–Jordan elimination.

(c) Which method involves fewer computations?

     Prove that if  and all the entries in A are integers, then all the entries in are integers.
25.

     Let  be a system of linear equations in unknowns with integer coefficients and integer constants. Prove that if
26.       , the solution has integer entries.

     Prove that if A is an invertible lower triangular matrix, then  is lower triangular.
27.

     Derive the last cofactor expansion listed in Formula 4.
28.
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