If #A=[(2,-1),(3,0),(1,2)]# and #B=[(3,2),(1,1)]#, find #2AB#?

1 Answer
May 9, 2017

#2AB=[(10,6),(18,12),(10,8)]#

Explanation:

As #A=[(2,-1),(3,0),(1,2)]# and #B=[(3,2),(1,1)]#

observe as #A# is a #3xx2# matrix and #B# is #2xx2# matrix,

we can multiply them as columns of #A# and rows of #B# are same and result will be a #3xx2# matrix.

In multiplication we multiply elements of #h^(th)# row of #A# with elements of #k^(th)# column of #B# to get the element of #k^(th)# column of #h^(th)# row.

Thus #2AB=2[(2xx3+(-1)xx1,2xx2+(-1)xx1),(3xx3+0xx1,3xx2+0xx1),(1xx3+2xx1,1xx2+2xx1)]#

= #2[(5,3),(9,6),(5,4)]=[(10,6),(18,12),(10,8)]#