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

Question 1159507: Find a non-zero 2×2 matrix such that:
[-9, -3] * [] = [0, 0]
[18, 6] [] [0, 0]
Answer by ikleyn(52802) (Show Source): You can put this solution on YOUR website!
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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  .




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  .



Thus, the second matrix can be taken as  .



Now you may check, making handle calculations, that

    * = ,   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.

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