Matrix maybe it can go in precalc section ?

[Jbreezy]

Homework Statement

Let A and B be matrices of the same size.
a.) prove the jth column of $A + B$ is $a_j + b_j$

Homework Equations

Where is i? In their question?

The Attempt at a Solution

What if you did this.

$A= \begin{pmatrix} a_{1j}\\ a_{2j}\\ a_{3j} \end{pmatrix}$

B = $\begin{pmatrix} b_{1j}\\ b_{2j}\\ b_{3j} \end{pmatrix}$

A+B = $\begin{pmatrix} a_{1j} + b_{1j}\\ a_{2j} + b_{2j}\\ a_{3j} + b_{3j} \end{pmatrix}$

But I still have i and they say prove that it is aj + bj
I hope that code is right for the matrix when I preview it is would not show. EDIT Why does my code not work ?

 

[SteamKing]

IMO, the question assumed that since the jth column of A + B was sought, it was naturally implied the index i would range from 1 ... n, where n is the number of rows in A and B.

 

[Jbreezy]

What is IMO. Am I correct or no?

 

[rcgldr]

Is this proof meant to be done with a computer program, or is it just a proof? If it's just a proof, it's not clear what is being sought here, there's a definition for adding matrices, and the syntax a_j means all values (all rows) in column j of the matrix A, and b_j means all values in column j of B. You do not need to define an "i", unless you're trying to create a program, depending on the programming language.

In a language called APL, indexes for a multi-dimension array are separated by ';', and an empty field means all of the indexes for that dimension. So in APL, a_j => A[ ; j ], and b_j => B[ ; j ], no "i" needed. For example:

 

[Jbreezy]

No program just what the question says prove that Let A and B be matrices of the same size.
a.) prove the jth column of A+B is aj+bj

So I just put them in matrices and added them to show that yeah it is aj + bj ...I mean idk that is what the question said exactly

 

[rcgldr]

No program just what the question says prove that Let A and B be matrices of the same size.
a.) prove the jth column of A+B is aj+bj

So I just put them in matrices and added them to show that yeah it is aj + bj ...

I'm not sure what constitutes "proof" since the statement is true based on the definitions of A+B and aj + bj.

 

[Jbreezy]

I'm not sure what constitutes "proof" since the statement is true based on the definitions of A+B and aj + bj.

Yeah I'm not sure I guess they wanted you to carry out the operation? I suppose.

 

[D H]

EDIT Why does my code not work ?

I fixed it for you. The problem was that a_i_j isn't valid TeX code. a_{ij} is valid, and that's what I assumed you wanted. If you wanted the j lower than the i you would need to use a_{i_j}.

 

[Jbreezy]

Oh thanks. It threw me off because I just copied and pasted the code from the "How to type maths equations" thing at the top of the forum. Thanks

 

[SteamKing]

IMO = in my opinion