Given a linear transformation, determine matrix A

WK95
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Homework Statement


LPE6kM6.png



Homework Equations



The Attempt at a Solution


What is M_2 supposed to be? Is A supposed to be the matrix that produces those above linear transformations?
 
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pretty much, yes. can you determine what the matrix is?
 
WK95 said:

Homework Statement


LPE6kM6.png



Homework Equations



The Attempt at a Solution


What is M_2 supposed to be? Is A supposed to be the matrix that produces those above linear transformations?
M2(R) is the set of 2 X 2 matrices with elements from the field of real numbers. Other notation I've seen is M2x2.
 
Once a basis has been specified, each linear transformation has a unique matrix representation. Think about the vectors that they gave you ##L## acting on. Do they form a basis? If so, how would they be linked to the form of the matrix?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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