If A=begin{bmatrix}1 & 2&0 1 & 1&01&4&0 end{bmatrix}, B=begin{bmatrix}1 & 2&3 1 & 1&-12&2&2 end{bmatrix} text{ and } C=begin{bmatrix}1 & 2&3 1 & 1&-11&1&1end{bmatrix}. Show that AB=AC text{ but } B neq C

smileycellist2 2020-11-08 Answered
If A=[120110140],B=[123111222] and C=[123111111]. Show that AB=AC but BC
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Expert Answer

odgovoreh
Answered 2020-11-09 Author has 107 answers
Step 1
Given data:
The first matrix is A=[120110140]
The second matrix is B=[123111222]
The third matrix is C=[123111111]
Step 2
The multiplication of AB matrices is,
AB=[120110140][123111222]
=[(1+2)(2+2)(32)(1+1)(2+1)(31)(1+4)(2+4)(34)]
=[341232561]
The multiplication of AC matrices is,
AC=[120110140][123111111]
=[(1+2)(2+2)(32)(1+1)(2+1)(31)(1+4)(2+4)(34)]
=[341232561]
The multiplication of AB and AC is equal.
Thus, AB=AC, but B not equal to C.
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