Each row of the N-row trapezoidal matrix is regarded as a row vector α 1, α 2, α 3. α n .

Assuming that the line vectors are linearly related, there are coefficients K 1, K2, K3...KN that are not all zero, so

K1* a1+k2 * a2+k3 * a3 ...+kn * an = 0 holds, that is to say, these n vectors can be expressed each other. Do you understand? , where 0 is a vector of 0 and its component is 0.

Considering the equation of each vector component (vector linear addition: vector linear operation only includes vector number multiplication and vector addition and subtraction, which can be converted into the operation of each vector component-you should know), it can be concluded that the above equation can be established only if k 1=k2=k3 ... =0. That is, it is linearly independent.