# matrix question help

• Aug 31st 2012, 10:15 PM
LaVsy
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?
• Sep 2nd 2012, 07:14 AM
LaVsy
Re: matrix question help
need help anyone ?
• Sep 2nd 2012, 08:54 AM
kalyanram
Re: matrix question help
This is how the matrix will look.
$\left( \begin{array}{cccccccc}r_1 & r_1 & r_1 & r_1& r_1&...&...&r_1\\r_1 & r_2 & r_2 & r_2& r_2&...&...&r_2\\r_1 & r_2 & r_3 & r_3& r_3&...&...&r_3\\r_1 & r_2 & r_3 & r_4& r_4&...&...&r_4\\r_1 & r_2 & r_3 & r_4& r_5&...&...&r_5\\... & ... & ... & ... & ... & ...& ... & ...\\... & ... & ... & ... & ... & ...& ... & ...\\r_1 & r_2 & r_3 & r_4 & r_5 & ...& ... & r_N\\ \end{array} \right)$

The argument goes like this for the first row and column the index of the elements will be $a_{1k}$ and $a_{k1}$ respectively so for all these elements we have $r_1$. Now consider the sub-matrix by removing the first row and first column which is $(N-1)$x $(N-1)$ 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.
• Sep 3rd 2012, 11:09 PM
LaVsy
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?
• Sep 4th 2012, 12:05 AM
kalyanram
Re: matrix question help
You are correct. The matrix is Symmetric.
~Kalyan.
• Oct 1st 2014, 09:32 AM
waihongbryanlee
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. :(