Down -> 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad
Intro ......
y, det(A) and det(A1 ) are also integers. Justify . [4pt] Problem 2. Problem 3. Justify your answer. Problem 1. (T) Solve Since A1 = AT and det(A) = det(AT ), but T T is onto. [each 3pt] (1) If T1 : R → R (F) 2 3 n m and T2 : R m → R are linear trans- k formations, A is a singular matrix. (3) If A is orthogonal, then neither is T2 T1 .연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안. Indicate whether the statement is true(T) or (5) If A is an n×n matrix, then neither is T2 T1 . Determine whether the linear transformation Solve Take T1 : R → R given by T1 (x, 1 = det(AA1 ) = det(A) det(A1 ) = (det(A))2 . (F) Solve Take k = 0, y) = (x, then TA : Rn → false(F). Determine whether the linear transformation Solve Take T1 : R → R given by T1 (x, and if the linear system Ax = b is consistent for every vector ......
Index & Contents
연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad
연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안.pdf 자료문서 (첨부파일).zip
[목차]
Problem 1. Indicate whether the statement is true(T) or (5) If A is an n×n matrix, and if the linear system Ax = b is consistent for every vector b in Rn , then TA : Rn → false(F). Justify your answer. [each 3pt] (1) If T1 : R → R (F)
2 3 n m
and T2 : R
m
→ R are linear trans-
k
formations, and if T1 is not onto, then neither is T2 T1 . Problem 3. Determine whether the linear transformation Solve Take T1 : R → R given by T1 (x, y) = (x, y, 0) is one-to-one and/or onto. Justify ...
Problem 1. Indicate whether the statement is true(T) or (5) If A is an n×n matrix, and if the linear system Ax = b is consistent for every vector b in Rn , then TA : Rn → false(F). Justify your answer. [each 3pt] (1) If T1 : R → R (F)
2 3 n m
and T2 : R
m
→ R are linear trans-
k
formations, and if T1 is not onto, then neither is T2 T1 . Problem 3. Determine whether the linear transformation Solve Take T1 : R → R given by T1 (x, y) = (x, y, 0) is one-to-one and/or onto. Justify your answer. [each 5pt] and T2 : R3 → R2 given by T2 (x, y, z) = (x, y). Then (1) T : R3 → R3 , given by T (x, y, z) = (4x, 2x + y, x T is not onto, but T T is onto.
1 2 1
3y). (2) If the characteristic polynomial of A is p(λ) = λ λn1 + λ, then A is a singular matrix. (T) Solve Since det(A) = (1)n p(0) = 0, A is a singular matrix. (3) If A is orthogonal, then (det(A))2 = 1. (T) Solve Since A1 = AT and det(A) = det(AT ), 1 = det(AA1 ) = det(A) det(A1 ) = (det(A))2 . (4) The determinant of an invertible matrix A is equal to ±1 if all of the entries of A and A1 are integers. (T) Solve Since all of the entries of A and A1 are integers, det(A) and det(A1 ) are also integers. Also, det(A) det(A1 ) = 1, hence det(A) = ±1. (5) If λ is an eigenvalue of A and x is an eigenvector of A corresponding to λ, then kx is also an eigenvector of A corresponding to λ. (F) Solve Take k = 0, then kx = 0 is not an eigenvector. (1) Show that T is linear. [4pt] Problem 2. Indicat…(생략)
연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안.pdf 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안.pdf 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안.pdf
DownLoad 연세대 2학기-선대시험-2차중간-모범답안 YR 연세대 연세대 선형대수학 선형대수학 2학기-선대시험-2차중간-모범답안 족보 YR YR DownLoad DownLoad 족보 족보 2학기-선대시험-2차중간-모범답안 선형대수학
Down -> 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad
Body Preview
(T) Solve Since A1 = AT and det(A) = det(AT ), 1 = det(AA1 ) = det(A) det(A1 ) = (det(A))2 .연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안. [each 5pt] and T2 : R3 → R2 given by T2 (x, y, z) = (x, y). [each 3pt] (1) If T1 : R → R (F) 2 3 n m and T2 : R m → R are linear trans- k formations, and if T1 is not onto, then neither is T2 T1 . 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad CS . 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad CS . (T) Solve Since det(A) = (1)n p(0) = 0, A is a singular matrix. Indicate whether the statement is true(T) or (5) If A is an n×n matrix, and if the linear system Ax = b is consistent for every vector b in Rn , then TA : Rn → false(F). (5) If λ is an eigenvalue of A and x is an eigenvector of A corresponding to λ, then kx is also an eigenvector of A corresponding to λ. 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad CS . (T) Solve Since all of the entries of A and A1 are integers, det(A) and det(A1 ) are also integers. Problem 3. [each 3pt] (1) If T1 : R → R (F) 2 3 n m and T2 : R m → R are linear trans- k formations, and if T1 is not onto, then neither is T2 T1 .zip [목차] Problem 1. Justify . Determine whether the linear transformation Solve Take T1 : R → R given by T1 (x, y) = (x, y, 0) is one-to-one and/or onto. Problem 1. 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad CS . (1) Show that T is linear. (F) Solve Take k = 0, then kx = 0 is not an eigenvector. (5) If λ is an eigenvalue of A and x is an eigenvector of A corresponding to λ, then kx is also an eigenvector of A corresponding to λ.연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad CS .. (3) If A is orthogonal, then (det(A))2 = 1. Then (1) T : R3 → R3 , given by T (x, y, z) = (4x, 2x + y, x T is not onto, but T T is onto. 1 2 1 3y). (1) Show that T is linear. (2) If the characteristic polynomial of A is p(λ) = λ λn1 + λ, then A is a singular matrix. 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad CS . (T) Solve Since A1 = AT and det(A) = det(AT ), 1 = det(AA1 ) = det(A) det(A1 ) = (det(A))2 .연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안.. Then (1) T : R3 → R3 , given by T (x, y, z) = (4x, 2x + y, x T is not onto, but T T is onto. (F) Solve Take k = 0, then kx = 0 is not an eigenvector.pdf 자료문서 (첨부파일). (2) If the characteristic polynomial of A is p(λ) = λ λn1 + λ, then A is a singular matrix. Also, det(A) det(A1 ) = 1, hence det(A) = ±1. 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad CS . Justify . (4) The determinant of an invertible matrix A is equal to ±1 if all of the entries of A and A1 are integer. Justify your answer. [4pt] Problem 2. Indicat…(생략) 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안. (3) If A is orthogonal, then (det(A))2 = 1. [each 5pt] and T2 : R3 → R2 given by T2 (x, y, z) = (x, y).pdf 자료문서 (첨부파일). Problem 3. Justify your answer. Indicate whether the statement is true(T) or (5) If A is an n×n matrix, and if the linear system Ax = b is consistent for every vector b in Rn , then TA : Rn → false(F). Indicat…(생략) 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안. 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad CS .. 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad CS .pdf.. Justify your answer. Problem 3. [each 3pt] (1) If T1 : R → R (F) 2 3 n m and T2 : R m → R are linear trans- k formations, and if T1 is not onto, then neither is T2 T1 . Also, det(A) det(A1 ) = 1, hence det(A) = ±1.pdf 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안.pdf 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안.pdf 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안. Determine whether the linear transformation Solve Take T1 : R → R given by T1 (x, y) = (x, y, 0) is one-to-one and/or onto.. 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad CS . [4pt] Problem 2. [each 3pt] (1) If T1 : R → R (F) 2 3 n m and T2 : R m → R are linear trans- k formations, and if T1 is not onto, then neither is T2 T1 . Indicate whether the statement is true(T) or (5) If A is an n×n matrix, and if the linear system Ax = b is consistent for every vector b in Rn , then TA : Rn → false(F). Determine whether the linear transformation Solve Take T1 : R → R given by T1 (x, y) = (x, y, 0) is one-to-one and/or onto. Problem 1. 1 2 1 3y). Problem 3. (4) The determinant of an invertible matrix A is equal to ±1 if all of the entries of A and A1 are integerJustify your answer. Justify your answer.zip [목차] Problem 1. (T) Solve Since all of the entries of A and A1 are integers, det(A) and det(A1 ) are also integers. (T) Solve Since det(A) = (1)n p(0) = 0, A is a singular matrix. 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad CS .pdf 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안. Indicate whether the statement is true(T) or (5) If A is an n×n matrix, and if the linear system Ax = b is consistent for every vector b in Rn , then TA : Rn → false(F). Determine whether the linear transformation Solve Take T1 : R → R given by T1 (x, y) = (x, y, 0) is one-to-one and/or onto.pdf. 연세대 선형대수학 족보 2학기-선대시험-2차중간-모범답안 DownLoad CS . Justify your answe.