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GATE Exam - Engineering Mathematics
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Linear Algebra




1:

Rank of the matrix A =

 
0 0 0 0
4 2 3 0
1 0 0 0
4 0 3 0
 

A.

0


B.

1


C.

2


D.

3


  Answer Report Discuss

2:

A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is


A.

A must be invertible


B.

b must be linearly depended on the columns of A


C.

b must be linearly independent of the columns of A


D.

None of these


  Answer Report Discuss

3:

Consider the following two statements:
I. The maximum number of linearly independent column vectors of a matrix A is called the rank of A.
II. If A is an n x n square matrix, it will be nonsingular is rank A = n.
With reference to the above statements, which of the following applies?


A.
Both the statements are false
B.
Both the statements are true
C.
I is true but II is false.
D.
I is false but II is true.
  Answer Report Discuss

4:

The system of linear equations
(4d - 1)x +y + z = 0
- y + z = 0
(4d - 1) z = 0
has a non-trivial solution, if d equals


A.

1/2


B.

1/4


C.

3/4


D.

1


  Answer Report Discuss

5:

The rank of a 3 x 3 matrix C (= AB), found by multiplying a non-zero column matrix A of size 3 x 1 and a non-zero row matrix B of size 1 x 3, is


A.

0


B.

1


C.

2


D.

3


  Answer Report Discuss

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