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###### Saurabh posted an Question
June 10, 2022 • 10:45 am 10 points
• IIT JAM
• Mathematics (MA)

# Let a = (aij) be a 10 x 10 matrix such that aij=1 for i≠ j and aii= α + 1, where α > 0. let λ and μ be the largest and the smallest eigenvalues of a, respective

Let A = (aij) be a 10 x 10 matrix such that aij=1 for i≠ j and aii= α + 1, where α > 0. Let λ and μ be the largest and the smallest Eigenvalues of A, respectively. If λ+μ = 24, then α equals

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• ##### Anonymous User

maximum eigen value sum of all row elements a+1+9 and minimum a+1-1 so a+10+a=24 2a=14 a=7

a+a+10=24 where a is smallest ev and a+10 is largest ev so, 2a=24-10= 14 => a= 7 and a+10=17

if digonal elements same a and reaming elements 1 then large eigen value sum of elements of a row and minimum is a-1

check for 2x2 matrix by taking digonal elements a=3 and reaming 1 so char eq (3-x)²-1=0 x²-6x+8=0; x=2,4 a-1 and sum of row a+1

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