Mathematics - I Mid - I, January - 2015
1.The rank of the matrix 
is
-
0
-
1
-
2
-
3
-
Answer: D
2.The system of equations x + y + z = –3, 3x + y – 2z = –2, 2x + 4y + 7z = 7 will have
-
Uniquie solution
-
Infinite number of solutions
-
Two solutions
-
No Solution
-
Answer: D
3.If the rank of the matrix 
is 2 then x =
-
0
-
1
-
4
-
3
-
Answer: C
4.If 5 nonhomogeneous equations are given in 4 unknowns. The system of equations AX = B is consistent then maximum possibble rank of A =
-
4
-
3
-
< 4
-
5
-
Answer: A
5.The symmetric part of the matrix 
when it is written as sum of symetric and skewsymmetric matrices is
Answer: D
6.If A = 
then the skew symmetric matrix Q, where A = P + iQ is
Answer: A
7.The Eigen values of the matrix 
are
-
1, 4
-
2, 3
-
-1 , 6
-
7, -2
-
Answer: C
8.If A = 
Then A−1 =
Answer: C
9.The eigen vector corresponding to λ = 1 of 
is
Answer: A
10.The index and signature of the quadratic form 10x2 + 2y2 + 5z2 − 4xy −10xz + 6yz
-
3, 1
-
2, 2
-
1, 3
-
1, 2
-
Answer: B
11.If the system of equations x + 2y + 3z = 0, 2x + Ky + 7z = 0,4 x +8 y +13 z = 0, possesses a nontrivial solution then K = ………………………
Answer: 4
12.The rank of the matrix 
is ………………………….
Answer: 2
13.If A is a matrix such that all the minors of order r + 1 are zero then the rank of A is
Answer: ≤ r
14.If the system of equations x + y + z = 0, 2x + 5y -2z = 0, x +7 y - K z = 0, possesses a nontrivial solution then K = ……………………
Answer: 7
15.If the determinant of A is of order 3 is 8, the trace of A is 7, and one of the eigen values is two then the other eigen values are …………………….
Answer: 1, 4
16.If the eigen values of A are 2 , 3 and 6 then the eigen values of the matrix A – 2I are ……………….
Answer: 0, 1, 4
17.The Eigen values of A = are ……………………………………….
Answer: 1, 2, 5
18.If λ3 −λ2 +λ−1 = 0 is the characteristic equation of A then A − 1 = …………………………
Answer: A2 − A+ I
19.If the eigen values of A ar-2 , 6 and 3 then the nature of XT AX is ……………….
Answer: indefinite
20.The eigen vector corresponding to 1 + i of 
is ……………………………….
Answer: 