GATE (TF) Textile 2015 Question Paper Solution | GATE/2015/TF/11

Question 11 (Textile Engineering & Fibre Science)

If 3 and 4 are two eigen values of A= \begin{bmatrix} 3 & a & b\\ e & 2 & d\\ e & f & 4 \end{bmatrix} for some real numbers a,b,c,d,e and f, then the third eigen value of A is __2__.

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Given-
A= \begin{bmatrix} 3 & a & b\\ e & 2 & d\\ e & f & 4 \end{bmatrix}
3 and 4 are two eigen value-
As we know-
Sum of the diagonal element of the matrix=Sum of the eigen value
Let,third eigen value=x
Then,
3+2+4=3+4+x
x=2 (Ans)

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