Linear Transformations and Matrices

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SUMMARY

The discussion focuses on the linear transformation L:P1 >> P1, specifically evaluating L(6t - 4) given L(t + 1) = 2t + 3 and L(t - 1) = 3t - 2. The correct approach to find L(6t - 4) involves expressing it as a linear combination of known transformations, specifically L(6t - 4) = A*(t + 1) + B*(t - 1). The values of A and B must be determined to compute the transformation accurately.

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hkus10
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Let L:P1 >> P1 be a linear transformation for which we know that L(t + 1) = 2t + 3 and L(t - 1) = 3t -2
a) Find L(6t-4)
I just want to check the way to calculate this question.
Is L(6t - 4) equal to 6*3t - 4*2 = 18t - 8? if not, how to calculate it?
 
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Not. Why would you think that would be a 'way to calculate it'? Is there any logic behind that at all? You want to express 6t-4 as a combination of things you know how to calculate, like t+1 and t-1. Write 6t-4=A*(t+1)+B*(t-1). Find A and B.
 

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