# Determine if the set of elements are linearly independent

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The set of all 2 x 2 real matrices constitutes a real vector space. Determine whether the given set of elements is linearly independent:

[ 2 3 ] , [ -1 2 ] ,[ 1 0 ]

[ 1 1 ] [ 0 0 ] [ 0 1 ]

https://brainmass.com/math/linear-algebra/determine-set-elements-linearly-independent-16065

#### Solution Preview

For the three 2x2 matrices to be linear independent, we need the following to be true...

(1) a*mat(2,3;1,1) + b*mat(-1,2;0,0) + c*mat(1,0;0,1) = 0 implies that a=b=c=0. (note: mat stands for matrix)

So, lets ...

#### Solution Summary

A step-by-step solution is provide for this problem. The student is walked through the process of determining linear independence. An example using three 2x2 matrices is given to illustrate this process.

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