mid-ex_sol

# mid-ex_sol - SOLUTIONS FOR MIDTERM 1 (10 points) : Find the...

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

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.

Unformatted text preview: SOLUTIONS FOR MIDTERM 1 (10 points) : Find the equation of the plane, containing the points (2 , 1 , 1), (1 , 1 ,- 1), and (0 , 3 , 3). The set of all points of the form (2 , 1 , 1) + t ( (2 , 1 , 1)- (1 , 1 ,- 1) ) + s ( (2 , 1 , 1)- (0 , 3 , 3) ) = (2 , 1 , 1) + t (1 , , 2) + s (2 ,- 2 ,- 2) = (2 + t + 2 s, 1- 2 s, 1 + 2 t- 2 s ) , with t, s ∈ R . 2 (10 points) : Show that { f ∈ F ([0 , 1] , R ) : f (0) = f (1) } is a subspace of F ([0 , 1] , R ). We have to show that V = { f ∈ F ([0 , 1] , R ) : f (0) = f (1) } is closed under addition and multiplication. That is, if f, g ∈ V , and c ∈ R , then cf and f + g also belong to V . To handle cf , note that [ cf ](0) = cf (0) = cf (1) = [ cf ](1), hence cf ∈ V . Similarly, [ f + g ](0) = f (0)+ g (0) = f (1)+ g (1) = [ f + g ](1), which implies f + g ∈ V . 3 (10 points) : Determine whether the polynomial x 3 + x + 2 can be expressed as a linear combination of x 3 + x 2- x + 1 and 2 x 3 + 3 x 2- 4 x + 1....
View Full Document

## This note was uploaded on 02/02/2012 for the course MATH 115A 262398211 taught by Professor Fuckhead during the Spring '10 term at UCLA.

### Page1 / 2

mid-ex_sol - SOLUTIONS FOR MIDTERM 1 (10 points) : Find the...

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

View Full Document
Ask a homework question - tutors are online