Linear Algebra
Mathematics 124 B Spring 2007
Problem Assignment # 4
Due Friday , March 30
1) Section 3.4: 28 (try constructing the matrix "column by column), 46 (there are many possible bases)
2) Section 4.1: 20, 22, 28, 34, 36
3) In P
2
,
let
Wbe the set of all polynomials p
๎
t
๎
such that p
๎
2
๎
๎
0
.
(a) Show that W
is
a subspace of P
2
.
(b) Find the dimension of and a basis for W.
4) A 2ร2 symmetric matrix A has the form A๎
๎
๎
๎
๎
๎
a b
b d
๎
๎
๎
๎
๎
. Let W be the set of all symmetric matrices in R
2
๎
2
.
(a) Show that W is a subspace of R
2
๎
2
.
(b) Find the dimension of and a basis for W.
5) A square matrix A is singular if it is not invertible. Let H be the set of all 2ร2 singular matrices.
(a) Does H contain the "zero element" of R
2
๎
2
?
(b) Is H closed to scalar multiplication ? Explain.
(c) Is H closed to addition? Explain.
(d) Is H a subspace of R
2
๎
2
? Explain.
(e) If your answer to (d) was "Yes," find the dimension of and a basis for H.
m124bhw4.nb
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