Hi , the problem is written like this:

In a basis (e1,e2,e3) in r^3

F1=(1,0,1) , F2 = (0,1,1) f3 = (1,1,0)

Show That (F1,f2,f3) is also a basis in r^3 and give the relationship Between

the coordinates in both of the basis. Determine the coordinates for e1 + 2*f3

My progress:

Well first i use two fornulas

Y= t^-1 * x (1)

This is the formula to find coordinates of f basis

Where y is the basis f:s coordinates , and where t^-1

is the inverse of the change of basis matrix, and x is. The coordinates which belong

To the basis e

X= t*y. (2) T is the change of basis matrix

So

First of all i put up t

T is. 1 0 1

0 1 1

1 1 0

I have put the rows as columns

I find t through gauss elimination and get

T inverse. Is

1/2. *. 1 -1 1

-1 1 1

1 1 -1

The NeXT step is finding the coordinates

So i begin with formula. (1)

X = e1. And because. E2 and E3 is 0

Therefore the coordinates for x Will be

(1,0,0)

I use x And multiply it with t inverse

And get. (1/2 , -1/2 , 1/2). This is wrong according to the answer

It should be. (1/2, -1/2, 5/2) this in (e)

NeXT i go on using formula (2)

I multiply t with 2f3

And get. (2,2,0)

I add (2,2,0) + (1,0,0) = (3,2,0) this is correct

What am i doing wrong? Is there à better

Way to Solve this problen , pls aid me

Anywa