Find T([3,1]) for Linear Transformation R2 to R3

In summary, a linear transformation is a mathematical function that preserves vector addition and scalar multiplication properties while mapping points from one vector space to another. R2 and R3 represent different dimensions in a vector space, with R2 being two-dimensional and R3 being three-dimensional. To find T([3,1]) for a linear transformation from R2 to R3, a specific transformation matrix is used to multiply the vector [3,1], allowing for visualization and analysis of the transformation's effects on other points in R2. While a linear transformation from R2 to R3 cannot be reversed, a reverse transformation from R3 to R2 can undo its effects.
  • #1
radiator
23
0
if you have R2 ----> R3
and T([1,1]) = (-1,0,-3) and T([1,-1])=(5,2,-5) How can you find T([3,1]) ??
 
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  • #2
T[3,1] = 2*T[1,1] + t[1,-1]
 
  • #3
Thank you
 

1. What is a linear transformation?

A linear transformation is a mathematical function that maps each point in one vector space to a specific point in another vector space while preserving vector addition and scalar multiplication properties.

2. What is the difference between R2 and R3?

R2 and R3 represent different dimensions in a vector space. R2 refers to a two-dimensional space, while R3 refers to a three-dimensional space. In R2, points can be represented using two coordinates (x,y), while in R3, points can be represented using three coordinates (x,y,z).

3. How do you find T([3,1]) for Linear Transformation R2 to R3?

To find T([3,1]) for a linear transformation from R2 to R3, you will need to use a specific transformation matrix. You will multiply the vector [3,1] by this matrix to get the resulting vector in R3. The transformation matrix will depend on the specific transformation being performed.

4. What is the purpose of finding T([3,1]) for Linear Transformation R2 to R3?

The purpose of finding T([3,1]) for a linear transformation from R2 to R3 is to understand how the transformation affects a specific point in the two-dimensional space. This can help in visualizing and analyzing the transformation and its effects on other points in R2.

5. Can a linear transformation from R2 to R3 be reversed?

No, a linear transformation from R2 to R3 cannot be reversed. This is because the transformation results in a change in the dimension of the vector space. However, it is possible to perform a reverse transformation from R3 to R2, which would essentially undo the effects of the original transformation.

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