{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw1_solu

# hw1_solu - Solutions for Selected problems of Homework 1 A...

This preview shows pages 1–3. Sign up to view the full content.

Solutions for Selected problems of Homework 1 A. Agarwal 1016-331 Linear Algebra-1 Spring 2009-10 1. Q22,P.14 Here is an algebraic way of finding w as a linear combination of u and v . Linear combination means, we have to find scalars c 1 , c 2 such that w = c 1 u + c 2 v . The vector equation will look like " 2 9 # = c 1 " - 2 3 # + c 2 " 2 1 # This gives us " 2 9 # = " - 2 c 1 + 2 c 2 3 c 1 + c 2 # Solving the system of equations will give us c 1 = 2 , c 2 = 3. 2. Q56(a),P.27 We will use the fact that || a || 2 = a · a || u + v || 2 + || u - v || 2 = ( u + v ) · ( u + v ) + ( u - v ) · ( u - v ) = ( u · u + u · v + v · u + v · v ) + ( u · u - u · v - v · u + v · v ) using the commutative property of the dot product = ( || u || 2 + 2 u · v + || v || 2 ) + ( || u || 2 - 2 u · v + || v || 2 ) = 2( || u || 2 + || v || 2 ) 3. Q60,P.27 Use the fact || u + v || 2 = || u || 2 + 2 u · v + || v || 2 that we established in the previous problem to get || u + v || = 3. 1

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

View Full Document
4. If k v k = 5 and k w k = 3, what are the largest and smallest values of k v - w k ? What are the largest and smallest values of v · w ? Solu: Let θ be the angle between v and w . Then v · w = k v kk w k cos θ = 15 cos θ . Using the same idea as in previous problems.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

hw1_solu - Solutions for Selected problems of Homework 1 A...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online