Let W be sub-space in dimension m of F^n (m < n). Show that there exist m - n homogeneous equations in n variables, so that-
W={(x_1,...x_n) | a_11*x_1+...+a_1n*x_n=0,...,
a_n-m*x_1+...+a_n-mn*x_n=0}
(x_1,...x_n) is column vector.
Let W be sub-space in dimension m of F^n (m < n). Show that there exist m - n homogeneous equations in n variables, so that-
W={(x_1,...x_n) | a_11*x_1+...+a_1n*x_n=0,...,
a_n-m*x_1+...+a_n-mn*x_n=0}
(x_1,...x_n) is column vector.