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TK
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Problem regarding binomials from programming, formula derivation.?
Lets say I have the following matlab code for illustration:
n = 0;
For w = 1:5
For x = w + 1:6
For y = x + 1:7
For z = y + 1:8
n = n + 1;
A(n,:) = [w x y z];
End
End
End
End
The result of A will produce sort of like a combinatorial matrix with 8C4 or 70 rows. By having this matrix, we can see that for any given row number n, we can refer to the matrix and obtain the values w,x,y,z for that row.
The problem is, if given a random row number between 1 to 70, can we find the values of w,x,y,z for that particular row without referring to the matrix? Meaning is there a formula or method that is able to input row number,n, and outputs values w,x,y,z?
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Extended Problems
The previous solution must be able to accommodate changes in the code.
An extension to this problem would be:
1) The solution must be able to cope if more variables/for-loops are added.
2) The solution must be able to cope if the limits for each variable changes, EG: 5,6,7,8 becomes 57,58,59,60
One condition is set, that is, the limits must always be consecutive with increments of one. For example in the code, w-5, x-6, y-7, z-8, are consecutive with increments of one.
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I have a problem understanding the classification of standard and non standard basis. The question is:
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...............[ 1 1 ]. [ 4 ] ... [ 3 ]
Match the properties of x = V*a
End of question.
We are given 4 choices to classify each sub question:
a) standard basis
b) non-standard basis
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* Ignore all full stops only, they're there for easier viewing
The subquestions are as follows:
1)
[ -1 ] , [ 1 ]
[ 1 ] .. [ 1 ]
2)
[ 5 ]
[ 3 ]
3)
[ 1 ] , [ 0 ]
[ 0 ] . [ 1 ]
4)
5i + 4j
5)
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. [ 1 ] ...... [ 1 ]
6)
[ -1 ]
[ 4 ]
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Thanks
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