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2009. 03. 25.

HW #1. 2009. 03. 25. 한양대학교 기계공학과 최적설계연구실 박 규 병. Generate a matrix A by setting A = round(10*rand(6)) and generate a vector b by setting b = round(20*(rand(6,1)-0.5)). 1 번 문제 (1/2). Since A was generated randomly, we would expect it to be nonsingular. The system Ax = b

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2009. 03. 25.

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  1. HW #1 2009. 03. 25. 한양대학교 기계공학과 최적설계연구실 박 규 병

  2. Generate a matrix A by setting A=round(10*rand(6)) and generate a vector b by setting b=round(20*(rand(6,1)-0.5)).

  3. 1번 문제 (1/2) • Since A was generated randomly, we would expect it to be nonsingular. The system Ax =b • should have a unique solution. (1) Find the solution using the “＼” operation. (2) Use MATLAB to compute the reduced row echelon form U of [A b].

  4. 1번 문제 (2/2) (3) How does the last column of U compare with the solution x ? (4) In exact arithmetic they should be the same. Why? Explain. • 컴퓨터연산은 연산할 수 있는 유효숫자가 한정되어 있어 실제 답과 차이를 보이게 된다. 하지만 (3)에서소수점 4째 자리까지만 고려할 경우 동일한 값이 나타날 수 있고 (5)에서는 유효숫자때문에 발생하는 실제 차이값을 보여준다. (5) Compute the difference U (:,7)-x using format long.

  5. 2번 문제 (1/1) Let us now change A so as to make it singular. Set A (:,3)=A (:,1:2)*[4 3]’ . (1) Use MATLAB to compute rref([A b]). (2) How many solutions will the system Ax=b have? Explain.  b가 Range(A)에 속하지 않으므로 본 system은 해가 없다. (CASE V)

  6. 3번 문제 (1/1) Set y =round(20*(rand(6,1)-0.5)) and c =A *y . (1) Why do we know that the system Ax =c must be consistent? Explain.  c가 Range(A)에 속하므로 본 system은 consistent이다. (CASE III) (2) Compute the reduced row echelon form U of [A c]. (3) How many solutions does the system Ax =c have?  c가 Range(A)에 속하므로 본 system은 Infinitely many solutions을 갖는다. (CASE IV)

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