Question

Find 2A + 3B.

A. [28 4.3]
[4.3 28]

B. [27 1.2]
[1.2 27]

C. [13 -9.2]
[-9.2 13]

D. not possible

Answer 1

http://openstudy.com/#/updates/4ecaec2be4b04e045ae8ed07

Answer 2

what level of math is this?

Answer 3

Algebra B.

Answer 4

Oh thats matrices thats easy if you have a calculator.....Do you have one?

Answer 5

*Ahem* a graphing calculator to be precise...

Answer 6

No I don't have a graphing calculator..

Answer 7

OK well, 2A is just A, with each element multiplied by 2
3B is B with all the elements multiplied by 3.

And to get 2A + 3B, you take the two matrices you just created in the previous steps and add together all the elements that are in the same positions (e.g., top left added to top left)

Answer 8

I still don't understand.

Answer 9

okay, do you understand how to get from A to 2A?

Answer 10

No, I don't understand matrices at all....

Answer 11

OK a matrix is just a set of number in an arrangement of rows and columns. "A" is a matrix of 4 numbers. To find "2A", you just multiply each of the four numbers by 2, giving you a matrix that still has 2 rows and 2 columns, but all the numbers are 2x what they were originally. does that make sense?

Answer 12

Alright, yes it does.

Answer 13

OK, so try now to compute 2A (by multiplying the A matrix by 2), and then compute 3B (by multiplying the B matrix by 3) and tel me what you get.

Answer 14

Okay for 2A, I got [10 -2]
[-2 10]

and for 3B I got [18 6.3]
[6.3 18]

Is that correct or incorrect?

Answer 15

hold on let me check

Answer 16

hmm, are we looking at the same problem? I have that A is
[ 28 4.3 ]
[ 4.3 28 ]

Answer 17

oh wait, sorry! I was looking at the answer selections, not the original problem.

Answer 18

I did them individually.. like the A column I multiplied all four numbers by 2, then for the B column I multiplied all four numbers by 3. So did I do that wrong then?

Answer 19

Sorry, my fault! You got it exactly right. (I was looking at the matrix at the top of this page, not the one in the link.)

Answer 20

OK, you're on a roll, you've computed 2A and 3B correctly. Now, to get 2A+3B, all you do is add together the numbers that are in the same place. for example, add the top-left number of 2A and the top-left number of 3B to get the top-left number of the answer. does that make sense?

Answer 21

I think it makes sense, so it would be: [28 4.3]
[4.3 28]
Right?

Answer 22

perfect!! see, you thought you didn't know anything about matrices but it turns out you're now a matrix expert.

Answer 23

Thank you so much for helping me understand it!! :) It was a BIG help!! :)

Answer 24

So for adding matrices there are 2 important rules, which are that you can only add together two matrices that are the same shape, i.e. have the same numbers of rows and columns. You can add a 2x4 matrix to a 2x4 matrix, but you can't add a 2x4 matrix to a 2x3 matrix or any other shape.

The other rule is that when you add two matrices, the answer will always be the same shape (number of rows and columns) as the two matrices you started with.

Does that make sense?

Answer 25

Yes it makes sense! Thank you again!! :)

Answer 26

So for example, if they asked you to add these two matrices:

[ 1 3 ]
[ 9 2 ]

plus

[ 1 3 5 ]
[ 2 9 3 ]

Then the answer would be "not possible", because those two matrices are not the same shape, which means you can't add them.

Answer 27

I got it! :) This helped me A LOT!!

Answer 28

Great!!! Have fun :-)