# We have matrix #A=[(2,x),(y,3)]# and #B=[(y,-3),(5,2x)]#, #A,BinMM_(2,2) (CC)#. How you find #x,y # such that #(A+xI_2)(B+yI_2)=[(-25,59),(2x+y^2,20)]# ?

##### 1 Answer

Given:

Compute

Compute

Substitute equation [1] and equation [2] into the given equation

Performing the multiplication:

We have two unknown values and we have 4 equation from which we may chose; let's use the two equations in column 2:

Subtract equation [4] from equation [3]:

Substitute -5 for x into equation [4]: