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affans
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Homework Statement
Let T: R2 -> R1 be given by T(x,y) = (y^2)x + (x^2)y.
Is T linear? justify your answer
Homework Equations
The Attempt at a Solution
Yes it is a linear mapping because both points map onto one point.
This is very distressing. Just about everything you say here is wrong. There are not two points being mapped to one. The single point (x,y) in R2 is mapped to a single point in R1. But, in any case, that has NOTHING to do with being "linear". Please review the definition of "linear mapping". (It is basically what waht said.)affans said:Homework Statement
Let T: R2 -> R1 be given by T(x,y) = (y^2)x + (x^2)y.
Is T linear? justify your answer
Homework Equations
The Attempt at a Solution
Yes it is a linear mapping because both points map onto one point.
A linear mapping, also known as a linear transformation, is a mathematical function that maps one vector space to another in a way that preserves the linear structure of the original space. This means that the mapping preserves addition and scalar multiplication.
A linear mapping can be represented by a matrix or by a set of equations. The matrix representation involves multiplying the original vector by a matrix, while the equation representation involves expressing the mapping in terms of variables and coefficients.
A linear mapping preserves the linear structure of a vector space, while a nonlinear mapping does not. This means that a nonlinear mapping does not preserve addition and scalar multiplication. In other words, the output of a nonlinear mapping is not a linear combination of the inputs.
Linear mapping is used in a variety of fields, including physics, engineering, economics, and computer science. Some examples of its applications include image and signal processing, machine learning, and control systems.
In data analysis, linear mapping can be used to transform data into a lower-dimensional space, making it easier to visualize and analyze. It can also be used to find patterns and relationships between variables, and to make predictions based on the data.