Find a basis for the vector space of all symmetric 3 x 3 matrices.

Step-by-step explanation:

We are given that vector space of all symmetric matrix

M(R)={

where a,b,c,d,e,f,g,h,i}

Let A=

A'=

A is symmetric

Then A'=A

=

a=a  , e=e,  i=i

a-a=0 , e-e=0,   i-i=0

b=d,  c=g  ,f=h

Hence, the matrix

Therefore, the basis are

There are three elements  to generate an element of vectors of all symmetric matrix matrix

=

i think this could be a possible answer (1 / 84) -1

good luck! : d

898.1666667

step-by-step explanation:

5389/6 = 898.1666667