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

=

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

it will cost dollar $540

the living room is 3 which means if we divide 325/3 then we get $108

therefore if 1part of the living room cost $108 and 3 costed $325

then total 5part of the room will cost 5*108 which gives $540