A First Course in Linear Algebra · Problem M20

Determinants — Robert Beezer

Mathematics — Linear Algebra · subspace-basis-dimension

Problem

M_{22}

is the vector space of

2 \times 2

matrices. Let

S_{22}

denote the set of all

2 \times 2

symmetric matrices. That is

S_{22} = \left\{ A \in M_{22} \mid A^t = A \right\}

1. Show that

S_{22}

is a subspace of

M_{22}

. 2. Exhibit a basis for

S_{22}

and prove that it has the required properties. 3. What is the dimension of

S_{22}