+0

# am i correct on these 2?

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3  if smeone could check my answers, thank you

Sep 17, 2019

#1
+3

ST   =

3   4        - 2  0      =       [ -6 - 16      0 + 20       =    [ - 22    20

-1 - 2       -  4  5                 2 + 8      0 +  10 ]                10   -10  ]

TS  =

-2   0       3   4       =         [ -6 + 0      -8 + 0           =    [  -6      -8

-4  -5      -1  -2                    -12 + 5    -16 + 10 ]              -7     -6 ]

They are not the same   [as we should expect, in general ]

BTW, Jenny.....here is an excellent site to check your work with these  :

http://matrix.reshish.com/multiplication.php   Sep 17, 2019
#2
+2

A  =  3 x 2

B  =  2 x 2

C =   1 x 3

D  =   2 x 1

Here's a rule        we can  multiply  martices  only   with the same  "inner" dimensions

And the resulting matrix wll be  the "outer" dimensions

For  example

Matrx 1    =    a  x  b

Matrix 2  =     b  x  c

So

M1     *     M2       =

[ a x b ]   *  [ b * c ]

We can multiply these because the  "inner dimensions"  [ the blue b's]  are the same

And the resulting matrix will have the dimensions of  a x c    [ the "outer" dimensions ]

So

BD  =   [2 x 2 ] * [ 2 x 1 ]  =  [ 2 x 1 ]

CA  = [ 1 x  3 ] * [ 3 x 2 ]    =  [ 1 x 2 ]

DC  = [  2 x1 ] *  [ 1 x 3 ]   =  [  2 x 3  ]   Sep 17, 2019
edited by CPhill  Sep 17, 2019
#3
+2

One more thing about matrix multiplication    .....the resulting matrix elements will tell you what row, column of each matrix to multiply to get a partcicular element

For  example.....we are multiplying  a 2 x 2  matrix by a 2 x 2 matix

The resulting matrix  will be a 2 x 2  with the following elements

[   a 11    a 12

a 21   a  22  ]

This tells you that  the   element   a mn   is obtained by multiplying the mth row of the first matrix by the nth column of the second

So....for example.....element a 11   is obtained by multiplying the first row of the first matrix by the first column of the second.....etc.   Sep 17, 2019