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Thread: Linear Algebra - Matrix transformations

  1. #1
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    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.
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  2. #2
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    Re: Linear Algebra - Matrix transformations

    Quote Originally Posted by MrJank View Post
    Hi, could you please give me some tips on how I can approach a, b and c.
    Linear Algebra - Matrix transformations-i3.png
    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.
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  3. #3
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    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.
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    Re: Linear Algebra - Matrix transformations

    Quote Originally Posted by HallsofIvy View Post
    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?
    Last edited by MrJank; Sep 16th 2018 at 05:40 AM.
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  5. #5
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    Re: Linear Algebra - Matrix transformations

    Quote Originally Posted by MrJank View Post
    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: $\{(1,1),~(2,4),~(3,9)\}$ .
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    Re: Linear Algebra - Matrix transformations

    Quote Originally Posted by Plato View Post
    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?
    Last edited by MrJank; Sep 16th 2018 at 05:58 AM.
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  7. #7
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    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.
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