A= 1 -2 B= -2 2
1 -1 -1 1
What is AB? (A x B)
Could anyone explain to me how to solve this problem in steps?? Thanks for your help. I need it!!!
2007-03-21 18:17:17 · 7 answers · asked by C 2 in Science & Mathematics ➔ Mathematics
matrice A is; top left: 1, top right: -2 bottom left: 1, bottom right -1. Matrice B is top left -2, top right: 2, bottom left -1, bottom right 1
2007-03-21 18:19:29 · update #1
Wikipedia has a good description (with pictures!) at:
http://en.wikipedia.org/wiki/Matrix_multiplication
2007-03-21 18:24:57 · answer #1 · answered by ymail493 5 · 0⤊ 0⤋
Since A has 2 rows and 2 columns (2x2) and B also has 2 rows and 2 columns (2x2), A*B is also 2x2. (To clarify, if A is 2x3 and B is 3x5, then A*B is 2x5.)
Since A is first you start with the top ROW of A and the left COLUMN of B.
Top row of A: [1, -2]
Left column of B:[-2, 2]
Multiply the first elements in each, multiply the second elements in each, then add the results.
(1)(-2) + (-2)(2) = -2 - 4 = -6
This is the element in the top row and left column of A*B.
Do the same for the top row of A and the right column of B, to get the element in the top row and right column of A*B.
The same needs to be done for the bottom row of A when paired with the left column of B and then the right column of B.
The result should be:
A*B = [-6 0]
[-1 1]
2007-03-22 01:29:55 · answer #2 · answered by polymac98 2 · 0⤊ 0⤋
The first step is to take row 1 in Matrix A and multiply it by column 1 in Matrix B.
(1*-2)+(-2*-1)
Then multiply row 1 by column 2.
(1*-2)+(-2*-1) (1*2) + (-2*1)
Do the same with row 2, and you end up with:
(1*-2)+(-2*-1) (1*2) + (-2*1)
(1*-2)+(-1*-1) (1*2) + (-1*1)
Now multiply the numbers out:
(-2)+(2) (-2)+(-2)
(-2)+(1) (2)+(-1)
Now just add.
[0 0]
[-1 1]
2007-03-22 01:29:56 · answer #3 · answered by andrea_bocelli_fan1 3 · 0⤊ 0⤋
you take top row and multiply by first column (by adding)
1 * (-2) + (-2) * (-1) = 0
Thats the first element of AB (AB11)
1* 2 + (-2) * 1 = 0 (second element AB12)
1 * (-2) + (-1)(-1) = 0 (AB21)
and so on
2007-03-22 01:22:33 · answer #4 · answered by gabriell_021 2 · 0⤊ 0⤋
[ 4 0 ]
[ 3 3 ]
2007-03-22 01:25:52 · answer #5 · answered by Anonymous · 0⤊ 0⤋
1 -2 X -2 2= 1x(-2)+(-2)x(-1) 1x(2)+(-2)x(1)
1 -1 -1 1 1x(-2)+(-1)x(-1) 1x(2)+(-1)x(1)
= 0 0
-1 1
2007-03-22 01:47:10 · answer #6 · answered by djin 2 · 0⤊ 0⤋
(A,B)X(E,F)=(A*E+B*G, A*F+B*H)
(C,D)X(G,H)=(C*E+D*G, C*F+D*H)
Basically you take the row vectors of the first matrix,( in this case
[A,B] and [C,D] respectively) and you multiply them by the column vectors of the second matrix (in this case [E,G] and [F,H]).
2007-03-22 01:30:46 · answer #7 · answered by the_really_good_son 1 · 0⤊ 0⤋