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Posted

Say I have a matrix

[a]

[c]

And I want to get a new matrix which has the elements

[0.7a]

[0.6b]

[0.4c],

Is there any way that I can multiply the original matrix by another matrix to get the matrix that I want?

Posted

The quotient matrix you want is the factor times the identity matrix, IOW a diagonal matrix with all diagonal elements equal to the factor:

 

f 0 0 0 0 0

0 f 0 0 0 0

0 0 f 0 0 0

0 0 0 f 0 0

0 0 0 0 f 0

0 0 0 0 0 f

 

Actually the above multiple of identity is not the unique answer if the matrix is singular. In this case you can add to it any matrix which, multiplied by the given one, gives the zero matrix. The sum will be an alternative answer.

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