Answer:
Let and
bases of V. The matrix of change from A to B is the matrix n×n whose columns are vectors columns of the coordinates of vectors
at base A.
The, we case correspond to find the coordinates of vectors of C,
at base B.
1. We need to find such that
Then we find these values solving the linear system
Using rows operation we obtain the echelon form of the matrix
now we use backward substitution
Then the coordinate vector of is
2. We need to find such that
Then we find these values solving the linear system
Using rows operation we obtain the echelon form of the matrix
now we use backward substitution
Then the coordinate vector of is
3. We need to find such that
Then we find these values solving the linear system
Using rows operation we obtain the echelon form of the matrix
now we use backward substitution
Then the coordinate vector of is
Then the change of basis matrix from B to C is