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Question 33970: (1)A=[-3 2] B= [0 2] (find AB and BA if possible)
[2 -2] [-2 4]
(2)A=[-2 3] B=[ 3 ] (find AB if possible)
[1 -2] [-2 ]
[0 0]
(3)A=[2 -2 4] B=[2 1 -3 0]
[1 0 -1] [0 -2 1 -2] (find AB if possible)
[2 1 3] [1 -1 0 2]
I am having trouble with these problems i hope you can help me
thank you
Brittny
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! THEY ARE ALL OF SAME MODEL .I WILL SHOW YOU ONE .YOU TRY OTHERS.COME BACK IF IN DIFFICULTY.
(1)A=[-3 2] B= [0 2] (find AB and BA if possible)
[2 -2] [-2 4]
FIRST CHECK COMPATABILITY...THAT IS FIND THE ORDER OF A (M,N) = (2,2) MATRIX HERE.
AND ORDER OF B (P,Q)= (2,2)..N SHOULD EQUAL P .THEN WE SAY THEY ARE COMPATABLE AND THEY CAN BE MULTIPLIED.OTHERWISE NOT.THE ANSWER WILL BE C (M,Q) MATRIX THEN .HERE WE HAVE N=2=P...SO THEY ARE COMPATABLE AND CAN BE MULTIPLIED.THE NSWER WILL BE M=2 AND Q=2...THAT IS C(2,2)MATRIX
NEXT HOW DO WE FIND C =....
E11,E12
E21,E22
E11 IS OBTAINED BY MULTIPLYING EACH ELEMENT OF ROW 1 OF A WITH EACH ELEMENT OF COLUMN 1 OF B AND ADDING THEM UP.THAT IS
E11=-3*0+2*-2=-4
E12 IS OBTAINED BY MULTIPLYING EACH ELEMENT OF ROW 1 OF A WITH EACH ELEMENT OF COLUMN 2 OF B AND ADDING THEM UP.THAT IS
E12=-3*2+2*4=2
E21 IS OBTAINED BY MULTIPLYING EACH ELEMENT OF ROW 2 OF A WITH EACH ELEMENT OF COLUMN 1 OF B AND ADDING THEM UP.THAT IS
E21=2*0+-2*-2=4
E22 IS OBTAINED BY MULTIPLYING EACH ELEMENT OF ROW 2 OF A WITH EACH ELEMENT OF COLUMN 2 OF B AND ADDING THEM UP.THAT IS
E22=2*2+-2*4=-4
HENCE THE ANSWER IS C=
-4,2
4,-4
(2)A=[-2 3] B=[ 3 ] (find AB if possible)
[1 -2] [-2 ]
[0 0]
(3)A=[2 -2 4] B=[2 1 -3 0]
[1 0 -1] [0 -2 1 -2] (find AB if possible)
[2 1 3] [1 -1 0 2]
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