# Thread: Linear Algebra - Matrix transformations

1. ## Linear Algebra - Matrix transformations

https://gyazo.com/f818a9b812029166bf8c1972a40d8431

Hi, could you please give me some tips on how I can approach a, b and c.

Thank you mathhelpforum for all the help.

2. ## Re: Linear Algebra - Matrix transformations

Originally Posted by MrJank
Hi, could you please give me some tips on how I can approach a, b and c.

You cannot expect us to do your work for you.
The set $[0,1]$ is not the set of numbers between zero & one, it is the set of numbers from zero to one.
The set $(0,1)$ is the set of numbers between zero & one.

You need to show us what you have tried as well as what you do not understand.

I will say that if you cannot do part a then you have not made effort to understand any of this.

3. ## Re: Linear Algebra - Matrix transformations

A lot of the time problems with understanding what a problem is asking is simply a matter of not having learned the basic definitions.

a) asks for a function that has domain {1, 2, 3}. Okay, what is the definition of "domain of a function"?

b) asks for a function that has codomain R and has image the interval [-1, 1] the set of numbers between -1 and 1 and -1 and 1 themselves (that is sometimes referred to as "the numbers between -1 and 1 inclusive"). Okay, what is the "codomain" of a function? What is the "image" of a function? Be careful that you understand the difference between the two!

c) asks for a function whose domain is Z (the set of integers) and whose codomain is $\displaystyle R^2$. Again, you need to look up the definitions of "domain" and "codomain" as well as being sure you understand what Z and $\displaystyle R^2$ are.

4. ## Re: Linear Algebra - Matrix transformations

Originally Posted by HallsofIvy
A lot of the time problems with understanding what a problem is asking is simply a matter of not having learned the basic definitions.

a) asks for a function that has domain {1, 2, 3}. Okay, what is the definition of "domain of a function"?

b) asks for a function that has codomain R and has image the interval [-1, 1] the set of numbers between -1 and 1 and -1 and 1 themselves (that is sometimes referred to as "the numbers between -1 and 1 inclusive"). Okay, what is the "codomain" of a function? What is the "image" of a function? Be careful that you understand the difference between the two!

c) asks for a function whose domain is Z (the set of integers) and whose codomain is $\displaystyle R^2$. Again, you need to look up the definitions of "domain" and "codomain" as well as being sure you understand what Z and $\displaystyle R^2$ are.
As I understand it, the domain of a function is the set of possible values that can be "fed" into the function. For (a), it is asking for an example of a function with the domain being the set {1,2,3}. Am I just supposed to come up with a function that can take the elements in this domain?

So,
f: {1,2,3} --> R^2, Defined by f(a) = [a 2a]

Is that valid?

5. ## Re: Linear Algebra - Matrix transformations

Originally Posted by MrJank
As I understand it, the domain of a function is the set of possible values that can be "fed" into the function. For (a), it is asking for an example of a function with the domain being the set {1,2,3}. Am I just supposed to come up with a function that can take the elements in this domain? In that case, would f(x) = x^2 be a valid answer?
Yes that is a function. I suspect the author expect a listing of the function.
In your example: $\{(1,1),~(2,4),~(3,9)\}$ .

6. ## Re: Linear Algebra - Matrix transformations

Originally Posted by Plato
Yes that is a function. I suspect the author expect a listing of the function.
In your example: $\{(1,1),~(2,4),~(3,9)\}$ .
Sorry I updated my function, is this still valid?

f: {1,2,3} --> R^2, Defined by f(a) = [a 2a] (supposed to be a 2x1 vector)

Is that valid?

And when you say listing, that will also be the codomain?

7. ## Re: Linear Algebra - Matrix transformations

A function, from set A to set B is a set of ordered pairs {(a, b)} where a is a member of set A and b is a member of set B. In the case that the relation is given by a formula, y= f(x), that set of ordered pairs can be written {(a, f(a)} where a is, again, a member of the domain. For your example, f(a)= [a 2a] that set of ordered pairs would be {(1, [1 2]), (2, [2, 4]), (3, [3 9])}. Yes, that is a function from {1, 2, 3} to R2.

No, that listing is NOT the "codomain". In this case the codomain is given as R2. The image is the set {[1 2], [2 4], [3 9]} of y- values.