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Let S = T : R3 —> R3 ; T is a linear transformation with T(1,0,1) = (1, 2, 3), T(1,2, 3) = (1,0,1)}. Then S is
- a)A singleton set
- b)A finite set containing more than one element
- c)A countable infinite set
- d)An uncountable set
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Let S = T : R3 —> R3 ; T is a linear transformation with T(1,...
Let S = {T : R3---> R3 such that T is a linear transformation with
T(1, 0, 1) = (1, 2, 3), T(1, 2, 3) = (1,0,1)}.
Then we can define the linear transformation for the third independent element in any way. Therefore, we can get uncountably many linear transformation.
T(1, 0, 1) = (1, 2, 3), T(1, 2, 3) = (1,0,1)}.
Then we can define the linear transformation for the third independent element in any way. Therefore, we can get uncountably many linear transformation.
Most Upvoted Answer
Let S = T : R3 —> R3 ; T is a linear transformation with T(1,...
In this notation, S represents a subspace and T represents a transformation. The subspace S is defined as the range of the transformation T, which means that S is the set of all possible outputs of T.
In other words, S is the set of all vectors in R3 that can be obtained by applying the transformation T to some vector in R3.
For example, if T is a linear transformation that rotates vectors in R3 by 90 degrees counterclockwise, then S would be the set of all vectors in R3 that can be obtained by rotating some vector by 90 degrees counterclockwise.
Note that S may not include all vectors in R3, as some vectors may not be reachable by applying the transformation T.
In other words, S is the set of all vectors in R3 that can be obtained by applying the transformation T to some vector in R3.
For example, if T is a linear transformation that rotates vectors in R3 by 90 degrees counterclockwise, then S would be the set of all vectors in R3 that can be obtained by rotating some vector by 90 degrees counterclockwise.
Note that S may not include all vectors in R3, as some vectors may not be reachable by applying the transformation T.
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Community Answer
Let S = T : R3 —> R3 ; T is a linear transformation with T(1,...
D)
An uncountable set
An uncountable set
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Let S = T : R3 —> R3 ; T is a linear transformation with T(1,0,1) = (1, 2, 3), T(1,2, 3) = (1,0,1)}. Then S isa)A singleton setb)A finite set containing more than one elementc)A countable infinite setd)An uncountable setCorrect answer is option 'D'. Can you explain this answer?
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