Page 7 - Engineering Mathematics Workbook_Final

Linear Algebra

(a) a = − 1 b = 0 24. Let A be a 4 4 non-singular matrix
and B be the matrix obtained from A by
(b) a = 1 b = 2 adding to its third row twice the first
)
−
1
det
(c) a = 0 b = 1 row. Then (2A B = __________
(d) a = − 1 b = 1 [MS 2005] (a) 2 (b) 4

 1 0 1 x 1 x  (c) 8 (d) 16
+
+
 
  0 1 1 1   [MS 2007]
22. Let P  =    .
+
+
 1 1 x 0 1 x  25. Let A, B be 2 2 matrices with real
  − =
  1 1 x 1 x 0   entries and assume that AB BA CI
+
+
for some constants C, where I is identity
Then the determinant of the matrix P is matrix. Then C is _______
______
(a) 0 (b) 1
3
(a) ( 3 x + ) 1 (c) 2 (d) 4

2
(b) ( 3 x + ) 1 [IISC 2007]
 a  
(c) ( 3 x + ) 1    
26. Let A =    1   where a is a real.
(d) ( x + 1 )(2x + ) 3 [MS 2005]   49 
Then A is invertible _____
23. Let AX = B be a non-homogeneous
2
system of linear equations. The (a) for all a  22
augmented matrix
 1 1 − 2 1 M 1  (b) for all a  180  2 49
 
( AB  ): −  1 2 3 − 1 M 0   . (c) for all a  22 (or) a  180  2
2
  49
   0 3 1 0 M − 1   
Which of the following statement is (d) for all rational values of a
true? [IISC 2007]

(a) Rank of A is 3 27. If A an n n matrix with real (or)
complex entries and A = 0 then ____
3
(b) The system has no solution.
3
(a)( + ) =0
(c) The system has unique solution.
(b) I + A is invertible
(d) The system has infinite number of
solution (c) I + A is not invertible

(d) necessarily A = 0
[MS 2006]
[IISC 2007]

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