Page 106 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
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Use part (a) of Theorem 1.6.3 to prove part (b).
26.
What restrictions must be placed on x and y for the following matrices to be invertible?
27.
(a)
(b)
(c)
28.
(a) If A is an matrix and if b is an matrix, what conditions would you impose to ensure
that the equation has a unique solution for x?
(b) Assuming that your conditions are satisfied, find a formula for the solution in terms of an
appropriate inverse.
Suppose that A is an invertible matrix. Must the system of equations have a unique
29. solution? Explain your reasoning.
Is it possible to have without B being the inverse of A? Explain your reasoning.
30.
Create a theorem by rewriting Theorem 1.6.5 in contrapositive form (see Exercise 34 of Section 1.4).
31.
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