申論題

3.(19%)下面的問題共有三個子题,(a)子题要清楚地寫出證明,(b)子题只要簡短扼要地回答 提问即可,(c)子題除提出答案外、還需寫出答案背後的推導。 Let A be any matrix in. Then, since rank(A) = dim(R(A)), the dimension of range of A, and R(A) = R(AA^T), we have the result rank(A) = rank(AA^T). Therefore, when replacing A by its QR factorization, we get rank(A) = rank(QRRT^TQ^TT).

(c) (8%) What does the obtained solution x = mean? Give your answer necessary explanations.