Page 9 - Engineering Mathematics Workbook_Final

Linear Algebra

(a) 1 (b) 2 x p q 1

(c) 25 (d) 50 a x r 1
36. If = 0 then x = ______
[MS 2010] a b x 1
a b c 1
 1 8 
33. An Eigen vector of the matrix    
  0 1  [IISC 2000]

is ___________ 37. The characteristic polynomial of the
 0 0 0 
T
T
1,2
(a) ( ) (b) (5,0 )    

matrix 1 0 1  is ____________

T
T
1,1
(c) (0,2 ) (d) ( )    0 1 0   
[MS 2011] 2 2
(a) ( x x + ) 1 (b) ( x x − ) 1
34. An Eigen vector of the matrix
 2 1 0  2
  (c) ( x x + ) 1 (d) ( x x − ) 1
2
 
 1 2 1
 
   0 0 2    [IISC 2002]

 1   0  38. Let A be a 3 3 real matrix. Suppose
        A = 0. Then A has ______
4


(a) 0 (b) 1
   
   0       0    (a) exactly two distinct real eigen values
 0   2  (b) exactly one non-zero real Eigen
        value


(c) 0 (d) 2
    (c) exactly 3 distinct real Eigen values
   1       2   
(d) No non-zero real eigen value
[MS 2012]
[IISC 2002]

35. Let A be a 3 3 real matrix with Eigen
values 1, 2, 3 and det B = A + − 1 A . 39. The determinant
2
Then the trace of the matrix B equal to x 0 x 1 x 2 x 3 x 4
________ x 0 x x 2 x 3 x 4
x x x x x = _________
91 95 0 1 3 4
(a) (b) x x x x x
6 6 0 1 2 4

97 101 x 0 x 1 x 2 x 3 x
(c) (d)
6 6

[MS 2013]

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