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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 $-1$
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Let the eigen values be $a,b$

Sum of Eigen Values = Trace(Diagonal Sum)

$\implies a+b = 2+5 = 7$

Product of Eigen Values = Det(A)

$\implies a\times b = 6$

Solving these we get eigenvalues as 1 and 6.

Option(B) is Correct.

answered by Boss (15.3k points)
edited 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.
(2-x)(5-x)-4=0 x=1,6
answered by Boss (14.2k points)