T is a 3-row, 4-column matrix, mapping 4-space into 3-space:
⎡ 2 1 1 0 ⎤
⎪ 3 2 2 2 ⎥
⎣ 6 0 -3 -1 ⎦
When applied to vector (1,0,0,0) we get:
⎡ 2 1 1 0 ⎤⎡1 ⎤ ⎡2⎤
⎪ 3 2 2 2 ⎥⎪0 ⎪=⎪3⎪
⎣ 6 0 -3 -1 ⎦⎪0 ⎪ ⎣6⎦
⎣0 ⎦
Note that column 1 is duplicated in the product, and this applies similarly to the other vectors, duplicating successive columns in T. Whichever row in the vector contains 1 causes the corresponding column in T to be duplicated in the product.