- #1

Puhseechee

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I'm asked to give an example of a matrix or linear transformation that has a given image or kernel.

Here are some examples...

## Homework Statement

Give an example of a matrix A such that im(A) is the plane with normal vector {1, 3, 2} in R^3.

Give an example of a linear transformation hose kernel is the line spanned by {-1, 1, 2}.

## Homework Equations

No equations per se.

Some definitions?

The image of a function consists of all the values the function takes in its target space. So if f(x) = y, y is the image.

And the kernel of T is the solution set of the linear system Ax = 0

## The Attempt at a Solution

For the problem with the normal vector, I've tried rotating the normal vector 90 degrees in various directions (since the plane in question is perpendicular, right?) and hoping that a two-columned matrix including two of those transformed vectors might be the answer, but I'm not even sure how to check my results.

For the problem with the kernel, I'm just stumped how to even begin.

These seem like relatively simple concepts, but I'm clearly missing something that I need to hurry up and just grasp. Your help would be much appreciated.