I have a few questions here, my main problem is not understanding the notations used, hence not understanding the questions.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

1. Do the vectors [tex]j_{1}[/tex]= (1,0,-1,2) and [tex]j_{2}[/tex]= (0,1,1,2) form a basis for the spaceW= {(a,b,c,d) la-b+c= 0, -2a- 2b+d=0} ?

2. Find a basis forW= { (a,b,c,d) :a-b+ 2d= 0 , 3a+c+ 3d= 0 }

3. Find the dimension of the following subspaces of [tex]\Re^{3}[/tex]

a) span { (1,0,1),(0,1,1),(2,0,0) }

b) span { (1,0,1),(2,2,4),(2,1,7),(-1,-1-2) }

4. Suppose that a subspaceW[tex]\subset[/tex] [tex]\Re^{3}[/tex] has a basis { (1,2,3),(1,0,1) }.

a)Is { (-1,-2,-3), (3,2,5) } a basis forW? Why?

2. Relevant equations

How do you do this? Is there a working? or can you solved this by inspection.

3. The attempt at a solution

1. i substitute each vector in a,b,c,d equation and find the equality, so happen when i substitute in all returns 0, which implies that it does form a basis. Is there a proper working for this, cause i can do this by inspection.

2. I was wondering forming a matrix and row reduced the matrix and get a linear dependence equation and plug in some value for c & d to find a & b.

1 -1 0 2 0 ~ 1 0 1/3 1 0

3 0 1 3 0 0 1 1/3 -1 0

So: a = -1/3c - d & b= d - 1/3c

Let c =1 and d =1

a= -1/3 (1) - 1 = -4/3 & b = 1 - 1/3 (1) = 2/3

so basis (-1/3,2/3,1,1)

3 & 4. No idea what to do.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Linear Algebra - Topic: Basis & Subspaces

**Physics Forums | Science Articles, Homework Help, Discussion**