Page 5 - Engineering Mathematics Workbook_Final

Linear Algebra

+
(a) (a d )  2 4    1 4 8   

11. The rank of the matrix 2 10 22 

+
(b) (a d ) = 2 4    0 4 12   
is __________
+
(c) (a d )  2 4
(a) 3 (b) 2

+
(d) (a d ) = 2 16 [IISC 2008] (c) 1 (d) 0
[JAM 2007]
8. For a square matrix A, Let Tr(A) denote
the sum of its diagonal entries. Let I be 12. The least positive integer n such that

the identity matrix. If A and B are 2 2     n
matrices with real entries such that   cos sin  
A = B = 0 and ( ) 0 then limit   4 4   is identity matrix
tr B 
of ( + ) as t → 0 is ______  − sin  cos   
( + )   4 4  
(a) 0 (b)  of order 2_____

tr A (a) 4 (b) 8
)
( +
(c) (d) det A B
tr B
(c) 12 (d) 16
[IISC 2008] [JAM 2008]

9. If A and B are 3 3 real matrices such 13. Let A be 10 10 matrix with each row
that rank (AB) = 1 then rank(BA) has exactly one entry equal to 1, the
cannot be _______ remaining nine entries of the row being

(a) 0 (b) 1 0. Which of the following is not a
passible value for det A.
(c) 2 (d) 3
(a) 0 (b) 1−
[JAM 2006]
(c) 10 (d) 1
10. Let A be a matrix of order 2 with real
entries such that AB = BA for an [IISC 2009]
matrices of order 2 then,
14. Consider the system of equations
(a) A is always the zero matrix
a x b y c z = d ,
+
+
1
1
1
1
=
R
I
(b) A  for some   a x b y c z = d ,
+
+
2
2
2
2
(c) A is always invertible a x b y c z = d where a , b , c ,
+
+
3
i
i
3
i
3
3

(d) A is never invertible [IISC 2007] d are real for 1 i  3. If
i

3