Linear Algebra and Lab 1

Course Information

Textbook: Contemporary Linear Algebra by Howard Anton and Robert C. Busby

Classes: Mondays and Thursdays 11am~1pm; 자2-424호

Labs: Time and place will be announced when necessary.

Grades: 2 Midterms (200 points), Final Exam (100 points), Homework, Quizzes and Labs (200 points)

Instructor's Office Hours: W 2~4 pm (Room 417), sy2kang@kangwon.ac.kr

Teaching Assistants: Jang, Deokgyu (장덕규) dkjang@kangwon.ac.kr (Room 419 )

Park, Joosung (박주성) js-park@kangwon.ac.kr (Room 419 )

Announcement

• 4/4 중간고사1 (Sections 1.1~3.3); 5/9 중간고사2 (Chapters 3 and 4); 6/10 기말고사(Chapters 6 and Sections 7.1~7.3)
• Office hours before final exam: 수요일 2~4pm; 박주성 (화요일 3~5pm, 수요일 1pm~); 장덕규 (화요일 1~3pm, 수요일 1~3pm); or you can ask any questions via email.

Topics covered in class

• 3/4 Section 1.1 Vectors and matrices; n-space
• 3/7 Section 1.2 Norm, dot product, orthogonality, orthonormality
• 3/11 Section 1.3 Lines and planes in the n-space
• 3/14 Section 2.1 Linear system: homogeneous linear system, consistent and inconsistent linear systems, elementary row operations
• 3/18 Section 2.2 Row reduction: row echelon form, reduced row echelon form, Gauss elimination method; Gauss-Jordan elimination method
• 3/21 Section 2.2 Dimension theorem for homogeneous systems; Section 3.1 Operations on matrices
• 3/25 Section 3.1 Matrix multiplication; inner and outer product of column matrices; Section 3.2 Vector space axioms for matrices, properties of matrix multiplication
• 3/28 Section 3.2 Identity matrix, invertible matrix, singular matrix, properties of transposes, traces and inverses; Section 3.3 Elementary matrix
• 4/1 Section 3.3 Characterizations of invertibility, inversion algorithm, consistency problem
• 4/8 Section 3.4 Subspaces, solution spaces, spanning sets, linearly independent sets, linearly dependent sets
• 4/11 Section 3,4 Linear independence and homogeneous linear system; Section 3.5 Solution set of a non-homogeneous linear system is an affine space
• 4/15 Section 3.5 Solution set of a non-homogeneous linear system, column space, hyperplane; Section 3.6 Diagonal matrix, triangular matrix
• 4/18 Section 3,6 Properties of triangular matrices, symmetric and skew-symmetric matrix; Section 3.8 Partitioned matrices and parallel processing
• 4/22 Section 3.7 LU-decomposition; Section 4.1 History of determinants
• 4/25 Section 4.1 Determinants, minor, cofactor expansion; Section 4.2 Properties of determinants
• 4/29 Section 4.2 Properties of determinants; Section 4.3 Adjoint of a matrix, formula for inverse
• 5/2 Section 4.3 Cramer's rule and applications
• 5/6 Section 4.4 Eigenvalues and eigenvectors
• 5/13 Section 6.1 Linear transformation
• 5/16 Sections 6.1 and 6.2 Geometry of linear transformations
• 5/20 Section 6.2 Orthogonal operators; Section 6.3 Kernel and range
• 5/23 Section 6.3 Kernel and range; Section 6.4 Composition and invertibility of linear transformation
• 5/27 Section 7.1 Basis and dimension
• 5/30 Section 7.2 Properties of bases
• 6/3 Section 7.3 The fundamental spaces of a matrix

Homework Assignments

• Set 1 (Due 3/11) Work on Cauchy-Schwarz inequality, triangle inequality, parallelogram law for vectors;
  • p.13 #6(a),10(b),12(c),16,20,22;
  • p.26 #4(b,d),8,10(a),12(c),18,20,22(a),24,26,28
• Set 2 (Due 3/18)
  • p.28 #P1,P3,P4, p.35 #2(a),6(b),8(c), 14,20,26,36,42(a), p.38 #D4
  • p.45 #4,10(b),12(a),14,16,20,22,26(b)
• Set 3 (Due 3/25)
  • p.59 #6,8,10,16,20,28,30,34,38,44, p.62 #D2,D5, p.63 #P1
  • p.90 #6(a,d,f),8(b,e),12,18,20,24,30,34
• Set 4 (Due 4/1)
  • p.91 #22 p.106 #2,5,8(b),16,18,20(b),26,30,32 p.108 #D1,D2
  • p.119 #2,4(d),6(d),8
• Suggested problems p.119 #9,11,13,15,19,22,23,25,27,29,31,34,P1,P8
• Set 5 (Due 4/15)
  • p.132 #4,6,8,10,14,16,18,20(a,b), 22(c),24,26,30; p.135 P2,P3
  • p.141 #2,4,16; p.142 P3
• Set 6 (Due 4/22)
  • p.141 #8,10(a,c),12,14,18,20; p.142 D2,D3,D4,P4
  • p.151 #2,4(b,c),6,8,12,16,20,22,24,26,28; p.152 D1,D10,P2
  • p.170 #2(a,b),6,8,10,12,14,18
• Set 7 (Due 4/29)
  • p.164 #4,6,8,10,12,14
  • p.182 #6,12(b,f),16,18,22,26(c,d),36;p.183 D4; p.184 P1
  • p.192 #6 Prove Lemma 4.2.0 given in class
• Set 8 (Due 5/6)
  • p.192 #8(b),10,14,20(a),22,24,26(a),28,32,34(c),35; p.194 D1,D4,D5,D8
  • p.207 #2,6,8,12,14,16,18,20,22,26,28,52; p.209 D6,D7
• Suggested problems p.221 odd-numbered problems, p.223 problems in Discussion and Discovery
• Set 9 (Due 5/20)
  • p.277 #2,4,6,8,10,12,14,16,18,20,22,24,26,30,34,36,38
  • p.293 #2,4,6,8,10,12,16,18
• Set 10 (Due 5/27)
  • p.295 #D2,D3,D4,D5
  • p.303 #2,4,6,8,10,12,16,18,19(b),20(b),21
  • p.315 #2,4,6,12,14,16,20,28
• Set 11 (Due 6/3)
  • p.334 #2,4,6,8,10,12, D4
  • p.340 #2,4,6,8,10,12,14,16,18
• ( Suggestions for Section 7.3) p.349 #2,4,8,10,12,16,18,20,22,24,26,28,30,32