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What matrix M changes the basis V1 = (1,1), V2 = (1,4) to the basis v1 = (2,5), v2 =

Chapter 5, Problem 5.6.8

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QUESTION:

What matrix M changes the basis V1 = (1,1), V2 = (1,4) to the basis v1 = (2,5), v2 = (1,4)? The columns of M come from expressing V1 and V2 as combinations mi jvi of the vs

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QUESTION:

What matrix M changes the basis V1 = (1,1), V2 = (1,4) to the basis v1 = (2,5), v2 = (1,4)? The columns of M come from expressing V1 and V2 as combinations mi jvi of the vs

ANSWER:

Step 1 of 3

Given vectors are  and with the basis vector as ,

On subtracting the vector  from

i.e.,

Thus,

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