Final answer:
The student's question regarding finding the values of c and d for a vector [30 20] in a new basis cannot be answered without additional information about the basis transformation. Typically, this would involve linear algebra techniques using the transformation matrix, but this information is not provided.
Step-by-step explanation:
The student is asking how to determine the values of c and d from a given vector represented in a new basis. The vector in the standard basis is presented as [30 20].
To find c and d, additional information is required about the transformation between the original basis and the new basis. Without this information, it is impossible to provide explicit values for c and d.
Since the context provided does not give enough details to solve for these unknowns, the best approach would be to look for any missing transformation information, or clarified basis vectors, to explicitly determine values for c and d.
In general, when we know the transformation that maps standard basis vectors to the new basis vectors, we can use linear algebra techniques, such as matrix operations, to find out the components c and d that correspond to the new basis.