M = \begin{Bmatrix} \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} : a = 2f, b = 2g + h, c = 3g - i, d = g + i, e = 3h \end{Bmatrix}
a) What is maximal possible dimension of the vector space M based on\nthe size of the vectors? What is the actual dimension?\nb) Determine a basis for M\nc) Determine coordinates of vector A = \begin{bmatrix} 2 & 7 & 2 \\ 6 & 9 & 1 \\ 2 & 3 & 4 \end{bmatrix} with respect to that\nbasis.