Page 8 - Engineering Mathematics Workbook_Final

Linear Algebra

28. If A is a 3 3 non zero matrix such that   6  

A = 0, then the number of non-zero (a) 0 
2

eigen values of A is _________     0    

(a) 0 (b) 1
 1 
(c) 2 (d) 3   6  
(b)   0  
[MS 2008]  
  0  

a
29. Let A = ( ) be an orthogonal matrix  
ij
1  2 + 1 
of order n such that a = ,   4  
ij
n  
(c)  0 
1 n n  
i = 1,2,........n. If a = 2   a then  0 
n i= 1 j= 1 ij    

n
  n ( ij a ) 2 = ____ (d) not determined uniquely
a −
i= 1 j= 1
[IISC 2006]
n + 1 n − 1
(a) (b) 31. The determinant
n n
+
+
a b c d e 1
n + 1 n − 1 b c d + a f 1
2
2
+
(c) (d)
n n c d a b g 1 =_________
+
+
+
[MS 2009] d + a b c h 1

30. Let M denote a 3 3 real matrix such (a) 0
 1 
     4   4  (b) 1
1
1
         

 
that M      5 =  1 
2 = 
2 , M 

+
+
) e
       5 (c) (a b )(c d + + f + g + h
       0      0   
3
3
 
 
 
 
+ + +
 6    (d) (a b c d )(e + f + g + ) h
 
then M   0  is [IISC 2006]
 
   0    32. Let P =   be a 50 50 matrix,

p
ij
where
p = ij min (  ,i j ) i j = , 1,2,......50 
then the rank of P is _________

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