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matrix question help
Consider a sequence of real numbers r1, r2 .... rn such that no two numbers are equal. Using these numbers, we create ( N x N) square matrix R such that the ( i, j)th element of R is given by
ai, j = rk, where k = min(i, j), i = 1,2,...., N; j = 1,2,....,N.
Write the elements of matrix R in terms of real numbers r1,r2,....,rn. Clearly show at least the top 4 x 4 and all the elements on the four corners.
And is this a symmetric matrix?

Re: matrix question help

Re: matrix question help
This is how the matrix will look.
$\displaystyle \left( \begin{array}{cccccccc}r_1 & r_1 & r_1 & r_1& r_1&...&...&r_1\\r_1 & r_2 & r_2 & r_2& r_2&...&...&r_2\\r_1 & r_2 & r_3 & r_3& r_3&...&...&r_3\\r_1 & r_2 & r_3 & r_4& r_4&...&...&r_4\\r_1 & r_2 & r_3 & r_4& r_5&...&...&r_5\\... & ... & ... & ... & ... & ...& ... & ...\\... & ... & ... & ... & ... & ...& ... & ...\\r_1 & r_2 & r_3 & r_4 & r_5 & ...& ... & r_N\\ \end{array} \right)$
The argument goes like this for the first row and column the index of the elements will be $\displaystyle a_{1k}$ and $\displaystyle a_{k1}$ respectively so for all these elements we have $\displaystyle r_1$. Now consider the submatrix by removing the first row and first column which is $\displaystyle (N1)$x$\displaystyle (N1)$ but the index of the elements will be starting from 2 and repeat the argument.
Now you can answer the second question if the matrix is symmetric or not?
~Kalyan.

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Re: matrix question help
Am I right to say that
R^(T) = r1 r1 r1 r1
r1 r2 r2 r2
r1 r2 r3 r3
r1 r2 r3 r4
So they are SYMMETRIC.
Am I correct?

Re: matrix question help
You are correct. The matrix is Symmetric.
~Kalyan.

Re: matrix question help
thanks for the solutions posted. Do you have the solutions for the remaining parts? I am taking the module TG1401 currently struggling to do CA1. :(