Vector Spaces

The set { (1,-2,6), (5,-10,30) } is

• Linearly dependent

• Linearly independent

• Basis

• None of the above

The subset { (1,-2), (2,9), (-4,3 } of   $R^2$  is 

• Linearly dependent  

• Linearly independent

• Basis

• None of the above

If A is 4 $\times$  5 matrix and its rank is 2 then nullity of matrix A will be

• 2

• 5

• 3

• 1

Dimension of set of 3 $\times$ 3  matrices with real entries is

• 6

• 9

• 3

• 0

If W is subspace of vector space v then

• dim W = dim V

• dim w $<$ dim V

• dim w $>$ dim V

• dim w $\le$ dim V

The dimension of subspace W = { (x,y,z) / x+y+z = 0 } of  $R^3$  is

• 1

• 3

• 2

• 0

If A is m $\times$ n matrix then which of the following is correct

• Row rank (A) = Column rank (A)

• Row rank (A)  $>$   Column rank (A)

• Row rank (A)  $<$   Column rank (A)

• None of the above

 If A is m  $\times$  n matrix then rank (A) + nullity (A) =

• mn

• m

• m + n

• n

 Is the set { (4,5,3), (1,0,2), (0,0,0) } is basis of  $R^3$ 

• Yes

• No 

• Can not be determined

• None of the above

 The set {1, x,  $x^2$ } is  

• Linearly Independent

• Linearly Dependent

• Spans  $P_2$ 

• 1 and 3 both