alias said:Homework Statement
T(a+bx+cx^2) = [b+c
a-c]
What is Ker(T)
Homework Equations
I don't the relevant equation(s). I know that the definition of the kernal of a LT is the set of all vectors that are mapped to 0 by T.
The Attempt at a Solution
What I need is a place to start or a hint at a first step.
For what values of a, b, and c is the vector <b + c, a - c> equal to the zero vector?alias said:Homework Statement
T(a+bx+cx^2) = [b+c
a-c]
What is Ker(T)
Homework Equations
I don't the relevant equation(s). I know that the definition of the kernal of a LT is the set of all vectors that are mapped to 0 by T.
The Attempt at a Solution
What I need is a place to start or a hint at a first step.
A linear transformation is a mathematical function that maps a vector from one vector space to another while preserving the basic structure of the vector space. It is a fundamental concept in linear algebra and has many applications in physics, engineering, and computer science.
P2 refers to the vector space of all polynomials with degree 2 or less, while R2 refers to the vector space of all 2-dimensional coordinate vectors. In the context of linear transformation, P2 is the domain of the function and R2 is the codomain.
A linear transformation can be represented by a matrix, which is a rectangular array of numbers. The columns of the matrix represent the images of the basis vectors in the codomain. The matrix can also represent the transformation of any vector in the domain by multiplying it by the matrix.
A linear transformation follows the properties of linearity, which means that the output is directly proportional to the input. On the other hand, a non-linear transformation does not follow these properties and can have a more complex relationship between the input and output.
Linear transformations have many applications in real life, such as in computer graphics, where they are used to rotate, scale, and translate images. They are also used in machine learning algorithms to transform data and make predictions. In physics, linear transformations are used to describe the motion of objects in 3-dimensional space.