Thread: Linear transformations and their inverse

A couple questions:

1)Consider the transformation T from R^2 to R^3 given by T [x1, x2] = x1[1, 2, 3] + x2[4, 5, 6]. Is this transformation linear? If so, find its matrix. Note: these matrices are vertical, I just didn't know how to type them vertically.

2)Find an n x m matrix A such that Ax = 3x, for all x in R^n. Note: x is a vector, I just didn't know how to put a vector arrow above it.

Thanks

Originally Posted by noles2188

A couple questions:

1)Consider the transformation T from R^2 to R^3 given by T [x1, x2] = x1[1, 2, 3] + x2[4, 5, 6]. Is this transformation linear? If so, find its matrix. Note: these matrices are vertical, I just didn't know how to type them vertically.

You show that transformation is linear, of course, by showing that the definition of "linear transformation" holds:
Is ?

To write it as a matrix, find and . That will give you the two columns of the matrix.

2)Find an n x m matrix A such that Ax = 3x, for all x in R^n. Note: x is a vector, I just didn't know how to put a vector arrow above it.

This is easy! Think of it as where I is the identity matrix.

Thanks

To see the LaTex code I used for these, click on each formula.