Figuring out kyle numbers for matrices/

[Witt27]

Homework Statement

http://www.math.harvard.edu/archive/21b_spring_09/faq.html
I'm having trouble understanding this explanation, particularly this part. "The Kyle numbers are 1, 2 because adding the first to 2 times the second column gives zero. "
Sorry for this basic question but I was wondering if someone can explain this particular part.

Homework Equations

NA

The Attempt at a Solution

NA

 

[ehild]

In principle, you have to find the Kernel of the matrix, that is the subspace the elements of which become zero by applying the linear transformation. In the example, the elements are multiples of the vector [1,2]^T. You can find the elements of the Kernel by row-reduction of the matrix, but I do not understand the sentence you cited "The Kyle numbers are 1, 2 because adding the first to 2 times the second column gives zero. "
Two times the first column added to the second one gives zero. So 1,2 are the numbers in the linear combination of the columns that produces null vector.