row 1 and column 1 signified by r1cl
:
r1c1=2(4)-4(3)=-4
r1c2=2(0)-4(-1)=4
r1c3=2(6)-4(5)=-8
r2c1=0(4)-1(3)=-3
r2c2=0(0)-1(-1)=1
r2c3=0(6)-1(5)=-5
:

Method 1:  Using the inverse:



Find the inverse of  

Do you know how to find the inverse of a 2x2 matrix?
If not post again asking how.  Or use method 2 below.

The inverse of  is 

Left-multiply both sides by this inverse:







-------------------------------

Method 2:  equating corresponding elements:



The right side is a 2x3 matrix.

The 2x2 matrix on the left side must be right 

multiplied by a 2x3 matrix to get a 2x3 matrix

Let  be the
required 2x3 matrix. Then, substituting,

(matrix(2,3,a,b,c,d,e,f))







We equate corresponding elements on the 2nd row on both
sides:

, , 

Substituting those:





We equate corresponding elements on the 1st row on both
sides:


So 





Edwin