How to Write Out a 2 x 3 Matrix in Linear Algebra?

[lolimcool]

hey guys, so I am new to linear algebra and is just learning matrix algebra

let A = a_ij be a 2 x 3 matrix, defined by a_ij = 2i + j. Write out A

would it just be
|1 2 3|
|4 5 6|

 

[magicarpet512]

No.
Remember that the i and j in your a_ij correspond to the ith row and the jth column.

 

[lolimcool]

what does that mean?
as in what does the 2i + j do to the function?

 

[magicarpet512]

It just like evaluating a regular function such as
f(x) = x^2 + 6x + 4 at x = 2.

So if you want to find the entry in the ith row and jth column then you evaluate
a_{i,j} = 2i + j at the ith row and jth column.

 

[lolimcool]

ok i don't know if I am following you
would it be something like this?
|3 4 5|
|5 6 7|

and if it is i still don't get it :S

 

[magicarpet512]

Thats exactly right!
If you don't get it then how did you get the right answer?

 

[lolimcool]

i think i get, would it be like this
|(2(1) + 1) (2(1) + 2) (2(1) + 3) |
|(2(2) + 1) (2(2) + 2) (2(2) + 3| so basically you plug the i and j value depending which position in the matrix you are in?

 

[magicarpet512]

exactly!