Question 366377

if  {{{A=(matrix(2,2,3,2,-4,1))}}}    
         
Find the values of m and n given that (AA)= mA+nA  
(A is a matrix of order 2×2)

AA = mA + nA
<pre>
Substituting:

{{{(matrix(2,2,3,2,-4,1))(matrix(2,2,3,2,-4,1))=m(matrix(2,2,3,2,-4,1))+n(matrix(2,2,3,2,-4,1))}}}

{{{(matrix(2,2,(3)(3)+(2)(-4),(3)(2)+(2)(1),(-4)(3)+(1)(-4),(-4)(3)+(1)(1)))=(matrix(2,2,3m,2m,-4m,1m))+(matrix(2,2,3n,2n,-4n,1n))}}}

{{{(matrix(2,2,9+(-8),6+2,-12+(-4),-8+1))=(matrix(2,2,3m+3n,2m+2n,-4m-4n,1m+1n))}}}
  
{{{(matrix(2,2,1,8,-16,-7))=(matrix(2,2,3m+3n,2m+2n,-4m-4n,1m+1n))}}}
   
Setting correponding elements equal:

{{{system(1=3m+3n,8=2m+2n,-16=-4m-4n,-7=m+n)}}}

There can be no solution to this system.

Sorry.  Did you copy something wrong?

Edwin</pre>