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GATE CSE 2015 Set 1 | Question: 36

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Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$. The eigenvalues of this matrix are $-1$ and $7.$ What are the  values of $a$ and $b$?

$\qquad A = \begin{pmatrix}1 & 4\\  b&a \end{pmatrix}$

  1. $a = 6, b = 4$
  2. $a = 4, b = 6$
  3. $a = 3, b = 5$
  4. $a = 5, b = 3 $
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Sum of eigen values    =  Trace of the matrix

-1+7 = 1+a

6 = 1 + a

a= 5
------------------------------------------------------------------------
 

product of eigen values = determinent of the matrix

-1 x 7 = a-4b

-7 = a-4b

-7 = 5-4b

4b = 5+7

4b = 12

b= 3

 

hope my answer helps u a lot

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