a) Find the basis and dimension of the subspace H = \begin{bmatrix} a-3b+6c \\ 5a+4d \\ b-2c-d \\ 5d \end{bmatrix} :a,b,c,d∈R​​

(b) What is rank of a matrix? Find the rank of a matrix A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 0 & 5 \end{bmatrix} ​