Question

given the matrices:
B=[ -2 3 2]
[ 1 3 3]

F=[ 0 2 -3]
[-2-3-3]
[-1 3 1]

what is BF?

Answer 1

BF=[-8 -7 -1;
-9 2 -9]

Answer 2

Are you cool with that or do you need to know why?

Answer 3

yes could you explain to me how you got that? my notes confuse me in the direction i multipy the numbers

Answer 4

First thing you must remember is: Row then Column
So first B has 2 rows and 3 columns so B is a 2x3 matrix
F has 3 rows and 3 columns. F is 3x3 matrix
To do BF the second number of B must be the same as F and the end result will be the outside numbers. So BF will be 2x3

Answer 5

Now. To get element 1x1 of the new matrix BF you get row 1 of B and multiply times column 1 of F.
So Element 1x1 will be: (-2)*(0)+(3)*(-2)+(2)*(-1) = 0-6-2=-8

Answer 6

To get element 1x2 (Row 1, column 2)
You multiply row 1 of B times column 2 of F
So element 1x2 is (-2)*(2)+(3)*(-3)+(2)*(3)=-4-9+6=-7

Answer 7

To get element 1x3 (Row 1, column 3)
You multiply row 1 of B times column 3 of F
So element 1x3 is (-2)*(-3)+(3)*(-3)+(2)*(1)=6-9+2=-1

Answer 8

Now. To get element 2x1 (Row 2, column 1)
of the new matrix BF you get row 2 of B and multiply times column 1 of F.
So Element 1x1 will be: (1)*(0)+(3)*(-2)+(3)*(-1) = 0-6-3=-9

Answer 9

Phew. I think you can do the last 2. Good luck. I hope that's clear.

Answer 10

yes it is, thank you very much!!