Question

94. Let I be the identity transformation of the finite dimensional vector spac
the nullity of I is :
(A) dim V
(B) 0
(C) 1
(D) None of these​

Answer 1

Answer:

94. Let I be the identity transformation of the finite dimensional vector spac

the nullity of I is :

(A) dim V

(B) 0

(C) 1

(D) None of these.

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Answer 2

Answer:

Option (b) is correct i.e. 0

Step-by-step explanation:

• Given that I is an identity transformation that means every element in the domain has a unique image in the codomain and also every element in the codomain has a preimage in the domain
• That means I is a one-one transformation
• We know that in one-one transformation only the identity of the domain maps to the identity of the codomain. That means the null space contains one and only one element that is identity
• And we know that the vector space with only identity as its element is zero-dimensional hence the nullity will be 0

Therefore the nullity of l would be 0 that is option (b)