# largest eigen value

138 views
Assume determinant of a $3\times3$ matrix is a prime number and trace is $15.$Largest eigen value is _______(Assume only positve eigen values)

edited

1 vote

Determinant is prime means product of these eigen values (3 because matrix is of dimension 3) is prime. When can product of 3 numbers be prime? Only when one of them is prime and other two are 1.

If you take two of them prime then the product becomes a non prime no. having factors as 1, those two prime numbers you multiplied and the number itself, thereby violating the  conditions of being a prime no.

Let E1,E2,E3. And E1=E2=1.

E1+E2+E3=15 (given)

1+1+E3=15

E3=13.

selected

## Related questions

1
219 views
1 vote
A 3 X 3 matrix P has 3 eigen values $-1 , 0.5 , 3$ What will be eigen values of $P^{2} + 2P + I$
Let $A$ be a $3\times 3$ matrix with Eigen values $-1,1,0$.Then $\mid A^{100}+I\mid$ is...