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The number of onto linear transformation from R3 to R4 is
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The number of onto linear transformation from R3 to R4isa)0b)1c)2d)3Co...
We need to find the number of onto linear transformation from R3 to R4.
Since dim R4 = 4 > 3 = dim R3. Therefore, there is no onto linear transformation from R3 to R4.
Suppose T : U ---> V be an onto linear transformation.
Then dim V ≤ dim U
Since dim R4 = 4 > 3 = dim R3. Therefore, there is no onto linear transformation from R3 to R4.
Suppose T : U ---> V be an onto linear transformation.
Then dim V ≤ dim U
Most Upvoted Answer
The number of onto linear transformation from R3 to R4isa)0b)1c)2d)3Co...
We need to find the number of onto linear transformation from R3 to R4.
Since dim R4 = 4 > 3 = dim R3. Therefore, there is no onto linear transformation from R3 to R4.
Suppose T : U ---> V be an onto linear transformation.
Then dim V ≤ dim U
Since dim R4 = 4 > 3 = dim R3. Therefore, there is no onto linear transformation from R3 to R4.
Suppose T : U ---> V be an onto linear transformation.
Then dim V ≤ dim U
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Community Answer
The number of onto linear transformation from R3 to R4isa)0b)1c)2d)3Co...
Explanation:
To find the number of onto linear transformations from R3 to R4, we need to consider the dimensions of the vector spaces involved.
Definition:
An onto linear transformation is a function that maps every element in the domain to a unique element in the codomain.
Dimensions of R3 and R4:
The vector space R3 represents all possible 3-dimensional vectors, while R4 represents all possible 4-dimensional vectors.
Key Point:
The dimension of a vector space is the number of vectors in a basis for that space.
Dimension of R3:
Since R3 represents 3-dimensional vectors, the dimension of R3 is 3.
Dimension of R4:
Similarly, since R4 represents 4-dimensional vectors, the dimension of R4 is 4.
Conditions for an onto linear transformation:
For a linear transformation from R3 to R4 to be onto, the dimension of the codomain (R4) must be greater than or equal to the dimension of the domain (R3).
Evaluating the options:
In this case, the dimension of the codomain (R4) is 4, which is greater than the dimension of the domain (R3), which is 3.
Conclusion:
Therefore, there are no onto linear transformations from R3 to R4. Hence, the correct answer is option 'A', which states that there are 0 onto linear transformations.
To find the number of onto linear transformations from R3 to R4, we need to consider the dimensions of the vector spaces involved.
Definition:
An onto linear transformation is a function that maps every element in the domain to a unique element in the codomain.
Dimensions of R3 and R4:
The vector space R3 represents all possible 3-dimensional vectors, while R4 represents all possible 4-dimensional vectors.
Key Point:
The dimension of a vector space is the number of vectors in a basis for that space.
Dimension of R3:
Since R3 represents 3-dimensional vectors, the dimension of R3 is 3.
Dimension of R4:
Similarly, since R4 represents 4-dimensional vectors, the dimension of R4 is 4.
Conditions for an onto linear transformation:
For a linear transformation from R3 to R4 to be onto, the dimension of the codomain (R4) must be greater than or equal to the dimension of the domain (R3).
Evaluating the options:
In this case, the dimension of the codomain (R4) is 4, which is greater than the dimension of the domain (R3), which is 3.
Conclusion:
Therefore, there are no onto linear transformations from R3 to R4. Hence, the correct answer is option 'A', which states that there are 0 onto linear transformations.
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The number of onto linear transformation from R3 to R4isa)0b)1c)2d)3Correct answer is option 'A'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The number of onto linear transformation from R3 to R4isa)0b)1c)2d)3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of onto linear transformation from R3 to R4isa)0b)1c)2d)3Correct answer is option 'A'. Can you explain this answer?.
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