SOLUTION: Find a non-zero 2×2 matrix such that: [-9, -3] * [] = [0, 0] [18, 6] [] [0, 0]

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Question 1159507: Find a non-zero 2×2 matrix such that:
[-9, -3] * [] = [0, 0]
[18, 6] [] [0, 0]
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find a non-zero 2×2 matrix such that:
[-9, -3] * [] = [0, 0]
[18, 6] [] [0, 0]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Looking at the first (2x2)-matrix, you may notice that its first column is three times the second column.


It tells you to take the first column of the second (2x2)-matrix as  %28matrix%282%2C1%2C+1%2C-3%29%29.




Looking again at the first (2x2)-matrix, you may notice that its second column is one third times the first column.


It tells you to take the second column of the second (2x2)-matrix as  %28matrix%282%2C1%2C+1%2F3%2C-1%29%29.



Thus, the second matrix can be taken as  %28matrix%282%2C2%2C+1%2C+1%2F3%2C++-3%2C+-1%29%29.



Now you may check, making handle calculations, that

    %28matrix%282%2C2%2C+-9%2C-3%2C++18%2C+6%29%29*%28matrix%282%2C2%2C+1%2C+1%2F3%2C++-3%2C+-1%29%29 = %28matrix%282%2C2%2C+0.0%2C+0.0%2C+0.0%2C+0.0%29%29,   QED.

This way, the problem is just solved, and one instance matrix is found.

But this solution is not a unique.

Every other matrix, c-times the found, where 'c' is any non-zero constant value, has the same property.