16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 2.6.6

Vector Spaces

Mathematics — Linear Algebra · row-space-basis-and-membership

Problem

Let

V

be the real vector space spanned by the rows of the matrix

A = \begin{bmatrix} 3 & 21 & 0 & 9 & 0 \\ 1 & 7 & -1 & -2 & -1 \\ 2 & 14 & 0 & 6 & 1 \\ 6 & 42 & -1 & 13 & 0 \end{bmatrix}.

(a) Find a basis for

V

. (b) Tell which vectors

(x_1, x_2, x_3, x_4, x_5)

are elements of

V

. (c) If

(x_1, x_2, x_3, x_4, x_5)

is in

V

what are its coordinates in the basis chosen in part (a)?