Candice said:Homework Statement
- What is the relation between the image of A and the image of A2 + A?
Homework Equations
The Attempt at a Solution
im (A^2 + A) for x (A^2+A) is within the image. Linear combination properties show A^2 x + A x. Not sure where to go from here
The relation between image(A) and image(A^2+A) is that they both represent the output values of a function or transformation applied to the same input values. In this case, the input values for both images are the elements of set A.
The images of A and A^2+A are different because they represent the output values of different functions or transformations. While the image of A represents the output of a function applied to the elements of set A, the image of A^2+A represents the output of a different function applied to the same input values.
Yes, it is possible for A and A^2+A to have the same image if the function or transformation applied to both sets results in the same output values. However, this is not always the case as different functions or transformations can result in different images.
A^2+A and A^2 are different as they represent the output values of different functions. A^2+A represents the output of a function applied to the elements of set A, while A^2 represents the output of a function applied to the elements of A multiplied by itself. Therefore, the input values for both images are different.
Comparing the images of A and A^2+A can provide insights into how different functions or transformations affect the output values of a set. It can also help identify patterns or relationships between the input and output values, which can be useful in understanding the behavior of functions and making predictions.