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If T : V2(R) → V3(R) defined as T(a, b) = (a + b , a-b ,b) is a linear transformation, Then nullity of T is
- a)0
- b)1
- c)2
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If T : V2(R) → V3(R) defined as T(a, b) = (a + b , a-b ,b) is a l...
We are given that a linear transformation T: V2(R) → V3(R) defined by
T(a, b) = (a + b , a - b, b).
We need to find the nullity of linear transformation T.
Let (a, b) ∈ ker T, Then
T(a,b)= (0,0,0)
Now using the definition of linear transformation, we get
(a + b, a - b , b) = (0, 0, 0)
Comparing the components of the co-ordinates, we get
a + b = 0, a - b = 0 , b = 0
Solving for a, b, we get
a = 0,6 = 0
Therefore,ker T = {(0, 0)}
Thus, dim (ker T) = 0, that is nullity of linear transformation T is zero.
T(a, b) = (a + b , a - b, b).
We need to find the nullity of linear transformation T.
Let (a, b) ∈ ker T, Then
T(a,b)= (0,0,0)
Now using the definition of linear transformation, we get
(a + b, a - b , b) = (0, 0, 0)
Comparing the components of the co-ordinates, we get
a + b = 0, a - b = 0 , b = 0
Solving for a, b, we get
a = 0,6 = 0
Therefore,ker T = {(0, 0)}
Thus, dim (ker T) = 0, that is nullity of linear transformation T is zero.
Most Upvoted Answer
If T : V2(R) → V3(R) defined as T(a, b) = (a + b , a-b ,b) is a l...
It seems that the question is incomplete. Please provide more information about what you would like to know about the linear transformation T in the vector space V2(R).
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