Answer:
║Y * * ║
║0 Y * ║
║0 0 Y║
║0 0 0║
Step-by-step explanation:
First, let's look at the information in the question:
The proof of the theorem proves that the columns, say, A and B must be independent.
In the matrix, there is linearity and the trivial solution would be [ 0, 0 , 0 , 0] for the matrix to exist. In other words, all the unknowns must be zero.
This establishes the fact that the matrix T needs to be independent for the matrix function, say T (x) to be one-to-one.
By definition, one-to-one is ker (T) = {0}
Thus, the null space is occupied only by the zero vector.
Note: if there was no linear independence in the vectors, the solution would not be zero in the vector.
