Page 6 - Engineering Mathematics Workbook_Final

Linear Algebra

b 1 c 1 d 1 17. Let P be a 4 4matrix whose det =

b 2 c 2 d  0 then the above 10.the determinant of 3P− is
2
−
−
b 3 c 3 d 3 (a) 810 (b) 30
system has ________ (c) 30 (d) 810

(a) atmost one solution [JAM 2012]

(b) always exactly one solution 18. Let A be a 5 5 matrix all of whose
eigen values are zero. Then which of the
(c) more than one but finitely many following statements is always true?
solution
T
(a) A = − A (b) A = − A
(d) infinitely many solutions
5
T
0
(c) A = A (d) A =
[IISC 2009]
[IISC 2010]

15. Let A be a 3 3 matrix with trace A = 3 19. Let A be n n matrix with real entries

and det A = 2. If 1 is an eigen value of such that A + 2 I =
A, then the Eigen values of the matrix 0. Then ______
A − 2I are (a) n is an odd integer
2

(i
(a) 1, 2 − ) 1 , − ( 2 i + ) 1 (b) n is an even integer
(c) n has to be 2
(i
(b) 1, 2 + ) 1 , − ( 2 i + ) 1
(d) n could be any positive integer
−
(i
(i
(c) 1, 2 − ) 1 , 2 + ) 1 [IISC 2011]
 1 2 3 4 5 1 
−
(i
(d) 1, 2 − ) 1 , − ( 2 i + ) 1    2 3 4 8 6 3  
[JAM 2011] 20. Let P  =   
 2 4 6 7 10 3 
 a b     4 7 10 14 16 7  
16. Consider the matrix A =     with
  c d  then the rank of the matrix P is ______
real entries suppose it has repeated eigen (a) 1 (b) 2
values. Pick the correct statement.
(c) 3 (d) 4
0
(a) bc =
[MS 2005]
(b) A is always a diagonal matrix
21. Consider the following equation
+
0
(c) det A x + y z = 3, x az b+ = ,
y + 2z = 3. This system has infinitely
(d) det A can take any real value
many number of solutions. If _____
[IISC 2009]

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