1. ## Determining Linear Independence

Three 2X2 matrices:

[2 3]
[1 1]

[-1 2]
[ 0 0]

[1 0]
[0 1]

How do I show if this set of elements in linearly dependent or not? Thanks,

Jim

2. ## lin dependance

For memory, two vectors in R^2 are linear dependant if and only if they one is a multiple of each other,

so something such as

[2 2] <---- v1
[1 1] <---- v2

(vector 1 is top row, vector 2 is bottom row)
would be linear dependant because v2 = 2(v1)

therefore,

[2 3] is linear independant as v2 isnt a multiple of v1
[1 1]

[-1 2] is linear dependant since v2 is the zero vector 0(v1) = v2
[ 0 0]

[1 0] is the identity matrix 2 therefore it is linear independant
[0 1]

Not sure if I'm 100% correct but if its urgent then I hope it helps

3. Hey Martinr,

Thanks! This is a big help.

Jim

4. Originally Posted by Jim Newt
Three 2X2 matrices:

[2 3]
[1 1]

[-1 2]
[ 0 0]

[1 0]
[0 1]

How do I show if this set of elements in linearly dependent or not? Thanks,

Jim
If you are considering the matrices themselves as vectors, clearly they are linearly independent, because 2 row 1 column co-ordinate is 0 in two matrices and non-zero in the remaining. No linear combination of 0s can give a 1.

5. But what if you were to consider the three matrices as a set instead of looking at each matrix as its own set? How would you go about determining whether the set of three matrices were independent or dependent?