Description

Quiz – 4

 
1 2 3
1. (3 points) Compute the value if x such that Det(A) = c where A
 
2 3 4
 
1 2 3
 
2. (3 points) Let x be such that Det(A) = c where A =  2 3 4 . Compute the determinant of matrix B given
 
 
4 5 x
 
2 4 6
  by B =  8 13 18 

 
 
4 5 x

3. (3 points) Let x and y be such that the maximum eigen value of A . Compute the maximum
 
 
4 y x
 −1 
eigen value of matrix B given by B =  2


4 2
1 y 
3

4 .
 
x − 2
4. (3 points) Let A ∈R3×3 and B ∈R3×3 be full rank matrices such that the eigen values of AB are 1,2 and 3. If Tr(BTB) = c and Tr , the minimum eigen value of BA is
5. (3 points) Let A3×3 be a skew symmetric matrix whose eigen values are 0, −cj. The imaginary part of the other eigen value of A is