The image of a linear transformation is the set of all possible outputs when the transformation is applied to all possible inputs. It is also known as the range or codomain of the linear transformation.
The image of a linear transformation is a subset of the codomain, which is the set of all possible outputs for the given domain. This means that the image is determined by the values of the domain that are transformed by the linear transformation.
Yes, it is possible for the image of a linear transformation to be larger than the domain. This can happen when the transformation maps multiple elements from the domain to the same element in the codomain, creating a larger image.
The image of a linear transformation is the set of all possible outputs, while the kernel is the set of all inputs that are mapped to the zero vector in the codomain. In other words, the kernel is the set of all inputs that result in an output of zero.
To find the image of a linear transformation, you can apply the transformation to all possible inputs in the domain and observe the resulting outputs. Alternatively, you can use linear algebra techniques to find the basis for the image and then determine all possible combinations of the basis vectors to form the image.