- #1

RyanH42

- 398

- 16

## Homework Statement

Let ##u_1,u_2,u_3## be a basis and let ##v_1=-u_1+u_2-u_3## , ## v_2=u_1+2u_2-u_3## , ##v_3=2u_1+u_3## show that ##v_1,v_2,v_3## is a basis and find the components of ##a=2u_1-u_3## in terms of ##v_1,v_2,v_3##

## Homework Equations

For basis vecor we need to clarify these vector are lineerly independet.We can understand linearly independent as make a matrix 3x3 and see the take the det of matrx. If det of matrix is not zero means linearly independent.

## The Attempt at a Solution

I take the determinant of ##v_1,v_2,v_3## and I found -1.It means linearly independent.It means they are basis vectors.Then I tried to show ##u_1=(1,0,0)## then I tried write it in terms of ##v## but I thought that there a lot way to do that or maybe wrong.

The answer is ##u_1=-2v_1+v_2-v_3## and ##u_2=3v_1-v_2+2v_3## and ##u_3=4v_1-2v_2+3v_3## and ##a=-8v_!+4v_2-5v_3##

Thanks