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

=

v = 1/3 a^2h

step-by-step explanation:

if the height is 57.7cm and the height of the slant edge is 18.2cm, then the volume is 1/3 a^2h.

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step-by-step explanation: