If T : Rn → Rn is given by T (x1, x2, ..., xn) = (x2 + x3, x3, ..., xn, 0) then write downthe matrix of T w.r.t. the standard basis of Rn

The transformation T : Rn → Rn is given by T (x1, x2, ..., xn) = (x2 + x3, x3, ..., xn, 0). We want to find the matrix representation of this transformation with respect to the standard basis of Rn.

The standard basis of Rn is {e1, e2, ..., en}, where ei is a vector with 1 in the i-th position and 0s elsewhere.

We can find the matrix representation by applying the transformation T to each basis vector and writing the result as a column in the matrix.

1. Apply T to e1: T(e1) = (0, 0, ..., 0) which is the zero vector. So the first column of the matrix is all zeros.

2. Apply T to e2: T(e2) = (1, 0, ..., 0). So the second column of the matrix is (1, 0, ..., 0).

3. Apply T to e3: T(e3) = (1, 1, 0, ..., 0). So the third column of the matrix is (1, 1, 0, ..., 0).

4. For i > 3, apply T to ei: T(e