Name:
Tuesday section time:
Student ID:
Math 20F  Linear Algebra  Winter 2003
Quiz #5 — February 18
(Do not discuss the quiz with students who haven’t taken it yet – until 8:00pm.)
(Do not calculate more than is necessary to answer a problem! For one of
these problems the answer(s) should be obvious from inspection.)
1. Let
v
1
=(1
,

1)
T
and
v
2
,
2)
T
,so
v
1
,
v
2
are a basis for
R
2
.
Let
x
=(3
,
2)
T
.
What are the coordinates
x
with respect to the basis
v
1
,
v
2
?
METHOD: You need to ﬁnd
a
1
,a
2
so that
x
1
=
a
1
v
1
+
a
2
v
2
. For this
you solve the matrix equation
±
11

12
¶±
a
1
a
2
¶
=
±
3
2
¶
. This can
be done either by row operations, or by inverting the
2
×
2
matrix.
ANSWER: The coordinates of
x
w.r.t. the basis
v
1
,
v
2
are
(
4
3
,
5
3
)
. That
is,
x
=
4
3
v
1
+
5
3
v
2
.
2. Let
This is the end of the preview. Sign up
to
access the rest of the document.
This homework help was uploaded on 01/23/2008 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.
 Winter '03
 BUSS
 Linear Algebra, Algebra

Click to edit the document details