3 votes 3 votes For the first one I have got -28 and 11 as the answer but for the matrix C I am not able to get the value of element c32. c31 = c33 = 6. Linear Algebra engineering-mathematics linear-algebra matrix eigen-value + – Shubhanshu asked Jul 24, 2017 Shubhanshu 765 views answer comment Share Follow See 1 comment See all 1 1 comment reply mitesh kumar commented Dec 13, 2018 reply Follow Share C32 can have any value because when we solve the characteristics equation by putting different eigen value then we get different value of b 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Sum of eigen values = trace of the matrix Product of eigen matrix = determinant of the matrix yes, for matrix A, values will be -28, 11 and for matrix C, values will be 6, x, 6 where x can be any real number. Manu Thakur answered Jul 24, 2017 Manu Thakur comment Share Follow See all 4 Comments See all 4 4 Comments reply Shubhanshu commented Jul 24, 2017 i edited by Shubhanshu Jul 24, 2017 reply Follow Share Yeah I think the value of x can be anything since it will not be going to affect the trace and the determinant of the matrix. But the answer is -11 and it is coming from the characteristic equation of Matrix i.e. $-\lambda^{3}+6\lambda^{2}-11\lambda+6$ Is there any relation between rows of the matrix and the characteristic equation of the matrix? 0 votes 0 votes MiNiPanda commented Dec 31, 2017 i edited by MiNiPanda Dec 31, 2017 reply Follow Share @manu thakur I am getting c32 as -11. As you said x can take any real value, I checked by placing the values 6,-12,6 in the matrix and solved it for the 3 eigen values. |A-I|, |A-2I| and |A-3I| should have been equal to zero but it is not so. Taking a=c31, b=c32, c=c33 a+b+c=1, a+2b+4c=8 and a+3b+9c=27 are you getting these equations? Can you please check? Thank you 0 votes 0 votes MiNiPanda commented Dec 31, 2017 reply Follow Share However if we choose shortcut like Trace = 0+0+c=1+2+3 which gives c=6 And, product of eigen values= determinant of the matrix, 1*2*3=b so 6= c , Then we cannot get value of b. 0 votes 0 votes Mahbub Alam commented Nov 16, 2018 reply Follow Share Nice explanation 0 votes 0 votes Please log in or register to add a comment.