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Math Help - Greetings and Please Direct Me To Correct Forum

  1. #1
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    Greetings and Please Direct Me To Correct Forum

    I am an old math student from way back when but have not used anything higher than say Algebra for years. Did very well in math in college but pursued another line of study - Information Systems.

    Here is my problem:

    I want to determine the entire value of a set of cells contained within a matrix that I determine based on dimensions.

    Each column of values is the same. In the first column all values are "2." All cells in the next columns will be +1 of the cells preceding column.

    Thus the values for column 1 are 2, Column 2 are 3, Column 3 are 4 and so on.

    Thus if I set the dimensions of the array of values to be x=10 and y=10 then the 10th column cell values will be worth 11 each.

    Is there a formula that applies to this?

    z=total value of all cell values in the array.

    x=total rows
    y=total columns

    cell value =2 for row 1 and +1 for each row thereafter.

    Example:

    x=4
    y=4

    2345
    2345
    2345
    2345

    total = 56

    Thus the function of x is to determine the amount of similar cell values in a particular column.

    The function of y is to determine the amount of columns in the array.

    Is this something that can be solved here or should I look for a programmer?
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  2. #2
    MHF Contributor
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    Re: Greetings and Please Direct Me To Correct Forum

    You can post such questions in Discrete Math or Math Topics forums.

    Each row is an arithmetic progression with the initial term a₁ = 2, common difference d = 1 and the number of terms n = y. The sum of the first n terms of arithmetic progression is (n/2)(2a₁ + (n-1)d) = (y/2)(4 + y - 1) = y(y + 3)/2. Since there are x rows, the sum of all values in the matrix is xy(y + 3)/2.

    Here are several remarks.

    Quote Originally Posted by wmp3662 View Post
    I want to determine the entire value of a set of cells contained within a matrix
    It is not clear whether "value" means sum, product or something else. You seem to need the sum of all numbers in the matrix.

    Quote Originally Posted by wmp3662 View Post
    Each column of values is the same.
    From what you say, it is not that each column is the same (as any other column), but in each column all numbers are the same.

    Quote Originally Posted by wmp3662 View Post
    x=total rows
    y=total columns
    In mathematics, usually x refers to horizontal dimension and y refers to vertical dimension.

    Quote Originally Posted by wmp3662 View Post
    cell value =2 for row 1 and +1 for each row thereafter.
    I though you said +1 for each column thereafter.
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  3. #3
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    Re: Greetings and Please Direct Me To Correct Forum

    First, thanks for working this out. I worked on it until 3AM and got the same formula you did: xy(y + 3)/2.

    Yes, each value in new columns increases by one of the last column. Thus 2 becomes 3 becomes 4 becomes 5, etc.

    And yes, I was looking for a way to sum up all of the values in a given array.

    Thanks for your help! We both solved it independently but you took less time in doing so I am guessing! (I took something like four hours using test cases of data and comparing differences in the progression of numbers).
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