Page 367 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
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(a) (2, 3, −7, 3)
(b) (0, 0, 0, 0)
(c) (1, 1, 1, 1)
(d) (−4, 6, −13, 4)
Find an equation for the plane spanned by the vectors and .
15.
Find parametric equations for the line spanned by the vector .
16.
Show that the solution vectors of a consistent nonhomogeneous system of m linear equations in n unknowns do not form
17. a subspace of .
Prove Theorem 5.2.4.
18.
Use Theorem 5.2.4 to show that , , , and ,
19. span the same subspace of . , and . Use
are points
A line L through the origin in can be represented by parametric equations of the form ,
20. these equations to show that L is a subspace of ; that is, show that if and
on L and k is any real number, then and are also points on L.
21. (For Readers Who Have Studied Calculus) Show that the following sets of functions are subspaces of
.
(a) all everywhere continuous functions
(b) all everywhere continuous functions
(c) all everywhere continuous functions that satisfy
