Let the transformation matrix be denoted by A:
The transformation T is defined as:
We are given two examples:1.
Let's verify this:
This contradicts the given information. There's an error in the problem statement. The result should be
, not
.2.
Let's verify this:
This also contradicts the given information. The result should be
, not
.**Conclusion:**The problem statement contains errors in the given transformations. The provided matrix A and the given transformations do not match. To correctly determine
, we need accurate information about the transformation's effect on at least three linearly independent vectors. With the current, contradictory information, a correct solution cannot be provided.