Science:Math Exam Resources/Courses/MATH152/April 2011/Question B 04 (b)/Solution 1

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The columns of a linear transformation matrix, A, are populated by the transformed vectors of each of the basis vectors. In this case the first column of A will be , the second, , and the third, . By computing these cross products, we get,

Therefore the linear transformation matrix A which corresponds to T is,

.

Notice if we wanted some sort of confirmation of our answer we can pick a random vector, say x=[3,4,7], compute and compute Ax and make sure they are the same thing.

and

which is indeed the same result.