Calculate the sum of odd numbers between 1 and 2001

pokvarilaap
2022-10-09
Answered

Calculate the sum of odd numbers between 1 and 2001

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Frida King

Answered 2022-10-10
Author has **8** answers

How many odd numbers are between 1 and 2001?

They form a sequence which general formula is

${a}_{n}=a+(n-1)\cdot d\Rightarrow 1999=3+(n-1)\cdot 2\Rightarrow n=999$

Their sum is

$S=\frac{n}{2}\cdot ({a}_{1}+{a}_{n})=\frac{999}{2}\cdot (3+1999)\Rightarrow S=999999$

They form a sequence which general formula is

${a}_{n}=a+(n-1)\cdot d\Rightarrow 1999=3+(n-1)\cdot 2\Rightarrow n=999$

Their sum is

$S=\frac{n}{2}\cdot ({a}_{1}+{a}_{n})=\frac{999}{2}\cdot (3+1999)\Rightarrow S=999999$

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There I have found from an old tutorial notes from a Linear Algebra course I am taking that I am finding the question rather cumbersome. I haven't come across any elementary matrices problem set in this way before. I have tried to using Gauss-Jordan Elimination to reduce matrix A, whilst performing the row operations on the corresponding elementary matrix. Although, I am unsure if this is the correct approach as the problem notes that RREF calculation is not necessary.

If [A|b] denotes the augmented matrix which corresponds to the system of linear equations

$w-y=-2$

$-w+x+z=5$

$2x-y+4z=1$ ,

determine the$3\times 3$ matrix E such that [EA|Eb] is the reduced row echelon form of [A|b]. Note: You are asked to calculate the matrix E but you are not asked to calculate the reduced row echelon form.

Any help on how to approach this question or determine the matrix E would be highly appreciated.

If [A|b] denotes the augmented matrix which corresponds to the system of linear equations

determine the

Any help on how to approach this question or determine the matrix E would be highly appreciated.