(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A problem on a linear algebra assignment is really confusing me. The problem is asking me to compute the distance from a vector to the image of a matrix (with orthogonal columns).

matrix A =

1 -2

4 6

2 -11

y=

3

-5

2

2. Relevant equations

dist(f,g) = norm( f - g ) ? possibly

3. The attempt at a solution

In the context of the actual course, the place I began was inner product spaces, seeing as that's really the only place where a distance computation is defined in the text. This is defined as dist(f,g) = norm( f - g ), where f and g are two elements of an inner product space. However, I wasn't sure where to go from there, or what operator I would use. I considered thinking about the matrix A as a plane and finding the normal vector, and computing a distance that way, but that seemed like a dead end as well. Any help would be appreciated.

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# Homework Help: Linear Algebra Problem - Distance from the Image of a Matrix to a Vector

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