Question

Please help me!! I need help on matrices.
this is the problem.

A= find 3A A= {7 2 9 }
{8 6 4 } then I did this A= {6 4}
{3 10 5 } {10 5}

I crossed multiplied and then I subtracted 30-40= -10

Do I now just times it by 3 because it says find 3A or did I do something wrong? please help.

Answer 1

(just checking the question)

Is A this 3x3 matrix ?

A= {7, 2, 9}
{8, 6, 4}
{3, 10, 5}

And you are trying to find 3A ?

Answer 2

to find 3A all you need to do is multiply EVERY component of the matrix A by 3

Answer 3

Yes! Then I did {6, 4} I crossed multiplied
{10, 5}

Answer 4

im not sure why you have cross multiplied, and i dont know where that 2x2 matrix has come from? it looks like a mix between a few different questions

Answer 5

ivonlorena, if you start out with a 3x3 matrix, you should end up with a 3x3 matrix

Answer 6

Alright so basically I multiply 7x3 then 2x3 then 9x3 and so on? or am I doing something wrong again

Answer 7

Wait I don't know :(

Answer 8

you are correct

multiply every number in the matrix by 3

Answer 9

and that's all you need to do to find 3A

Answer 10

so after I multiply each number by 3 what do I do next?

Answer 11

you're done after that

Answer 12

if all you were trying to find is 3A , and you have multiplied all the elements of A by three, then you are done.

Answer 13

Thank you so much UnkleRhaukus and jim_thompson5910!

Answer 14

I also need help on this one if you don't mind..

Find A+B where B=
{ 1, 1, 1}
{ 1, 1, 1}
{ 1, 1, 1} do I do the same thing?

Answer 15

now you are adding the matrices

so you add up the corresponding elements

Answer 16

A= {7, 2, 9}
{8, 6, 4}
{3, 10, 5}

B= { 1, 1, 1}
{ 1, 1, 1}
{ 1, 1, 1}

Answer 17

So in the upper right hand corner for instance, you'll have 9+1 = 10

The answer will be a 3x3 matrix and in the upper right hand corner of the answer matrix will have 10 in it. The other entries are found the same way (by adding up the corresponding elements)

Answer 18

So it would be?
{8, 3, 10}
{9, 6, 5}
{4, 11, 6}

Answer 19

everything is good, but the very center

it's not 6, it should be 7

Answer 20

oh woops that was an accident lol

Answer 21

that's ok

Answer 22

So in the last one it says Find 2(AC) where c=
{-3 -3 -3}
{-3 -3 -3}
{-3 -3 -3}

Answer 23

ok first you need to multiply matrix A with matrix C

however, multiplication isn't as simple as just multiplying the corresponding elements (like you do with addition). Matrix multiplication is a bit trickier. Are you familiar with it?

Answer 24

Wait nevermind I guess I'm not familiar with it

Answer 25

It was something like this but I don't know if this is a different kind of problem

Answer 26

that's a determinant, which is different

Answer 27

First off, we have to see if we can even multiply A and C

A is a 3x3 matrix
C is a 3x3 matrix


A has 3 columns, C has 3 rows. Because these '3's match up, we can multiply A and C

The final result will be a 3x3 matrix (the 3's are drawn from the first 3 of A and the last 3 of C)
-----------------------------

The way this is done is that each element in the final matrix will be found separately.

To find the element in row1, column1 of the final matrix, you would multiply the elements of row 1 of A with the corresponding elements of the column 1 in C

After you find all these products, you'll add them up to get the result for row1, column1

Answer 28

this image is a good way of thinking about it

http://cnx.org/content/m32159/1.4/matrixMultiply.png

Answer 29

I don't think I understand I ended up with 729. I think I did it completely wrong

Answer 30

what are the elements in the first row of matrix A?

Answer 31

-3 -3 -3?

Answer 32

that's matrix C

Answer 33

Omg I get it now I know what I did wrong.

Answer 34

Okay let me do it again. I'm sorry.

Answer 35

Are the first elements 7, 2, 9 or 7, 8, 3?

Answer 36

we look at row 1 of matrix A, so 7,2,9

Answer 37

column 1 of matrix C is -3, -3, -3

Answer 38

multiply those corresponding elements together

7(-3) = -21
2(-3) = -6
9(-3) = -27

then add up those products

-21 + (-6) + (-27) = -54

Answer 39

the result of -54 is the element that goes in row1, colum1 of the answer matrix

this needs to be done 8 more times (9 times total because have 9 elements in AC)

Answer 40

8x-3=-24
6x-3=-18
4x-3=-12 all together will be -54. So then I put that next to my other answer.

Answer 41

In the same row1, column 1?

Answer 42

notice how you're focusing on row 2 of matrix A

if you picked on column 1 of matrix C, then -54 will go in row2, column1 of AC

Answer 43

But I thought it was supposed to be done 9 more times.

Answer 44

it is, once for each entry in AC

matrix AC is a 3x3 matrix (9 entries total)

Answer 45

row1, column1 for AC is done by picking on row 1 from A, column 1 from C

row2, column1 for AC is done by picking on row 2 from A, column 1 from C

etc etc

Answer 46

So then it would just be -54? all of them?

Answer 47

Let me check, one moment

Answer 48

Yes, every result I'm getting is -54

However, it's always a good idea to go through and compute all the entries (so you can get practice)

Answer 49

anyways, after you get AC, you double everything in AC to get 2(AC)

Answer 50

So -108?

Answer 51

every entry will have -108, correct

Answer 52

so in the end, you'll have a 3x3 matrix filled with nothing but -108

Answer 53

Thank you very much for your help I understand now :)

Answer 54

you're welcome, I'm glad you do