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+7 votes
476 views

What are the eigenvalues of the following $2\times 2$ matrix? $$\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$$

  1. -1 and 1
  2. 1 and 6
  3. 2 and 5
  4. 4 and -1
asked in Linear Algebra by Boss (18k points) | 476 views

2 Answers

+14 votes
Best answer

Let the eigen values be a,b

Sum of Eigen Values = Trace(Diagonal Sum)

 => a+b = 2+5 = 7

Product of Eigen Values = Det(A)  

 => a.b = 6

Solving these we  get 1 and 6.. So, Option(B) is Correct ..

answered by Boss (15.2k points)
selected by
0
how did you derived this?
+1
these are famous properties..
0
will this work as check for matrices of size grater than 2*2
+1
always, for n*n matrices.
+3 votes
(2-x)(5-x)-4=0 x=1,6
answered by Boss (14.1k points)


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