Prove that the set of all real ( 2 × 2 ) symmetric matrices is a subspace of the vector space of all real ( 2 × 2 ) matrices. Find a basis for this subspace (see Exercise 26 of section 5.3) 26. Show that the set W of all symmetric ( 3 × 3 ) matrices is a subspace of the vector space of all ( 3 × 3 ) matrices. Find a spanning set for W .
Prove that the set of all real ( 2 × 2 ) symmetric matrices is a subspace of the vector space of all real ( 2 × 2 ) matrices. Find a basis for this subspace (see Exercise 26 of section 5.3) 26. Show that the set W of all symmetric ( 3 × 3 ) matrices is a subspace of the vector space of all ( 3 × 3 ) matrices. Find a spanning set for W .
Prove that the set of all real
(
2
×
2
)
symmetric matrices is a subspace of the vector space of all real
(
2
×
2
)
matrices. Find a basis for this subspace (see Exercise 26 of section 5.3)
26.
Show that the set
W
of all symmetric
(
3
×
3
)
matrices is a subspace of the vector space of all
(
3
×
3
)
matrices. Find a spanning set for
W
.
Definition Definition Matrix whose transpose is equal to itself. For a symmetric matrix A, A=AT.
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