Show that (K1 +K2)A =K1A+K2A?

If A= 0 1 2
|2 3 4|
4 5 6
and K1 =I, K2 = 2 show that (K1 +K2)A =K1A+K2A?

1 Answer
Apr 7, 2018

Answer:

See below.

Explanation:

#bbA=[(0,1,2),(2,3,4),(4,5,6)]#

#K1=[(1,0,0),(0,1,0),(0,0,1)]#

#(K1+K2)bbA=[(1,0,0),(0,1,0),(0,0,1)][(0,1,2),(2,3,4),(4,5,6)]+2[(0,1,2),(2,3,4),(4,5,6)]#

#=[(0,1,2),(2,3,4),(4,5,6)]+[(0,2,4),(4,6,8),(8,10,12)]=color(blue)([(0,3,6),(6,9,12),(12,15,18)]#

#K1bbA+K2bbA=[(1,0,0),(0,1,0),(0,0,1)][(0,1,2),(2,3,4),(4,5,6)]+2[(0,1,2),(2,3,4),(4,5,6)]#

#=[(0,1,2),(2,3,4),(4,5,6)]+[(0,2,4),(4,6,8),(8,10,12)]=color(blue)([(0,3,6),(6,9,12),(12,15,18)]#