Page 105 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
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18.
19.
Consider the matrices
20.
(a) Show that the equation can be rewritten as and use this result to solve for x.
(b) Solve .
Solve the following matrix equation for X.
21.
In each part, determine whether the homogeneous system has a nontrivial solution (without using pencil and paper); then state
22. whether the given matrix is invertible.
(a)
(b)
Let be a homogeneous system of n linear equations in n unknowns that has only the trivial solution. Show that if k is
23. any positive integer, then the system also has only the trivial solution.
Let be a homogeneous system of n linear equations in n unknowns, and let Q be an invertible matrix. Show that
24. has just the trivial solution if and only if has just the trivial solution.
Let be any consistent system of linear equations, and let be a fixed solution. Show that every solution to the system
25. can be written in the form , where is a solution . Show also that every matrix of this form is a solution.
