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Match the following concepts with the correct definitions:

1. T is a one-to-one function from R3 to R3
2. T is an onto function from R3 R 3 to R3
3. T is a function from R3 R 3 to R3

A. For every y in R3, there is a unique x in R3 such that T(x)=y.
B. For every x in R3, there is a y in R3 such that T(x)=y.
C. For every y in R3, there is at most one x in R3 such that T(x)=y.
D. For every y y in R3 R 3 , there is a x x in R3 R 3 such that T(x)=y T ( x ) = y .

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abidemiokin

Answer:

1- A

2- B

3-D

Explanation:

Mappings can be represented by

T:A->B where A is the domain and B is the codomains. We have different types of mapping such as;

One-one mapping- This means that all the element in the domain has a unique element in the co-domain.

Onto mapping is a mapping where all the elements in the codomains has a pre image in the domain.

Let y be our domain and x be the codomains

Given the mapping, T:R3->R3

A one-one mapping is if for every y in R3, there is a unique element in R3 such that T(x) = y

An onto mapping occur if for every x in R3 there is a y in R3

A function means for every y in R3, there is x in R3 that is T(x) = y

The matching of the concepts with the correct definitions:

1. T should be a one-to-one function = For each and every y in R3 it should be unique.

2. T should be onto function = For every x in R3

3. T should be function = For every y in R3

D. It stands for transformation which is both one-to-one and onto.

Matching:

1. T should be a one-to-one function that lies from R3 to R3 should be matched with unique x in R3.

2. T should be onto function that lies from R3 to Re should be matched with every R in R3.

3. T should be a function from R3 to R3 should be matched with most one x in R3.

D. It stands for transformation which is both one-to-one and onto.

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