2. Prove that the given set B is a basis for the given vector space V. And then, determine if

the given vector v is in V. If so, find the coordinate vector of ✔ with respect to B.

0

0

2

=

{ (² 9). (²₂2) · ( )· ()}.

1

(a) B=

(b) B=

V = M2x2 (R), v =

-1

=

{ ( ≤ 9) · ( 7 )) }

Span(B),

-1

1

(c) B = {1,1 + 2X, 1+ 2X +3X², 1+ 2X +3X² + 4X³}, V = R3(X), V = 8X³

V =

=

5

(₁2)

1 2 3

1 2 3