math110s-hw4

# math110s-hw4 - MATH 110 LINEAR ALGEBRA SPRING 2007/08...

This preview shows pages 1–2. Sign up to view the full content.

MATH 110: LINEAR ALGEBRA SPRING 2007/08 PROBLEM SET 4 If V is a vector space over F , we will write dim F ( V ) for the dimension of V when we wish to emphasize the ﬁeld of scalars. For example, dim C ( C 3 ) = 3 and dim R ( C 3 ) = 6. 1. Let W 1 , W 2 be subspaces of V such that V = W 1 W 2 . Let W be a subspace of V . Show that if W 1 W or W 2 W , then W = ( W W 1 ) ( W W 2 ) . Is this still true if we omit the condition ‘ W 1 W or W 2 W ’? 2. For the following vector spaces V , ﬁnd the coordinate representation of the respective elements. (a) V = P 2 = { ax 2 + bx + c | a,b,c R } . Find [ p ( x )] B where p ( x ) = 2 x 2 - 5 x + 6 , B = [1 ,x - 1 , ( x - 1) 2 ] . (b) V = R 2 × 2 . Find [ A ] B where A = ± 2 3 4 - 7 ² , B = ±± 1 1 1 1 ² , ± 0 - 1 1 0 ² , ± 1 - 1 0 0 ² , ± 1 0 0 0 ²² . (c) V = R 2 . Let θ R be ﬁxed. Find [ v ] B where v = ± x y ² , B = ±± cos θ sin θ ² , ± - sin θ cos θ ²² .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 08/01/2008 for the course MATH 110 taught by Professor Gurevitch during the Spring '08 term at Berkeley.

### Page1 / 2

math110s-hw4 - MATH 110 LINEAR ALGEBRA SPRING 2007/08...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online