HW #

Homework problems

Due date



Cumulative Final Exam on Tuesday, May 10th. (Solution published)
Training set of problems (don't forget about other problems in the corresponding quizzes(!), HWs and examples in the text):
0) One.III.1, p. 51: 1.7 (a,d), 1.8 (a,b,c), 1.9 (a,b,d);
1) Two.III.1, p. 114: 1.23 (a), 1.24 (a);
2) Three.I.1, p. 164: 1.13 (a,c); Three.II.1, p. 179: 1.17 (a,b,c), 1.18 (a,b), 1.19 (a);
3) Three.II.2, p. 190: 2.22 (a,d), 2.23 (a,b);
4) Three.IV.4, p. 234: 4.14, 4.15, 4.16 (d,f), 4.17;
5) Three.V.1, p. 239: 1.7 (a,d), 1.9 (b,c); Three.V.2, p. 245: 2.12 (a,b), 2.24 (a);
6) Four.I.2, p. 299: 2.7, 2.9;
7) Four.III.1, p. 327: 1.13, 1.14, 1.16(a,b), 1.17(a,b), 1.21;
8) Five.II.2, p. 356: 2.6, 2.7 (a), 2.14, 2.15;
9) Five.II.3, p. 362: 3.20 (a,d,e), 3.21 (a,b), 3.24 (a,b);
10) Three.VI.2, p. 256: 2.9, 2.10, 2.11.


13

Quiz09 on Tuesday, May 3rd. (Solution published) Topic: GramSchmidt ortogonalization process.
Quiz10 on Thursday, May 5th. (Solution published) Topic: Least Squares method (Study this!).
Three.VI.1, p. 251: 1.7, 1.8, 1.15, 1.18, 1.19;
Three.VI.2, p. 256: 2.9, 2.10, 2.11, 2.14;
Three.VI.3, p. 264: 3.10 (a,c), 3.11(a,d,f), 3.19, 3.23.
Additional reading (just for fun). MATLAB for Linear Algebra.

May 3rd, 2011, class time.

12

Quiz08 on Thursday, April 28st. (Solution published) Topic: Eigenvalues and eigenvectors.
Four.I.4, p. 315: 4.10, 4.11(a,b), 4.12(a,b);
Four.III.1, p. 327: 1.13, 1.14, 1.16(a,b), 1.17(a,b), 1.19, 1.20, 1.21, 1.27;
Addition to the homework. Complex numbers.
Five.II.1, p. 352: 1.4, 1.7, 1.10;
Five.II.2, p. 356: 2.6, 2.7 (a), 2.8, 2.11, 2.15;
Five.II.3, p. 362: 3.20 (a,d,e), 3.21 (a,b), 3.24 (a,b), 3.25, 3.29, 3.34, 3.40.

April 26th, 2011, class time.

1011

Quiz08 on Thursday, April 21st, is canceled
Four.I.3, p. 308: 3.14(a,b), 3.15(a), 3.16, 3.22, 3.25, 3.28, 3.30, 3.34;
Four.II.1, p. 321: 1.8(a,c), 1.9, 1.12(a,c), 1.19, 1.26.

April 19th, 2011, class time.



Quiz07 on Thursday, April 14th. (Solution published) Topic: determinants.
Exam 2 on Tuesday, April 12th. (Solution published) Topics: all covered material since Exam 1, before Four.I.3.
As usual, no calculators or books allowed. You can prepare a page of reference of any formulae etc. you like.
Training set of problems for Exam 2:
Three.II.2, p. 190: 2.23 (a,b);
Three.III.1, p. 200: 1.17 (a,c);
Three.III.2, p. 207: 2.9 (c), 2.13;
Also review Quiz 05;
Three.IV.4, p. 234: 4.16 (d,f);
Three.V.1, p. 239: 1.7 (a,d), 1.9 (b,c);
Three.V.2, p. 245: 2.12 (a,b), 2.24 (a);Have a look at the solution of the quiz 06!
Four.I.2, p. 299: 2.7, 2.9;
Also review the nullspace and how to find a basis in the null space for a transformation given by the matrix. Here is an example, study it thoroughly!

None.

9

Quiz06 on Thursday, April 7th. (Solution published) Topic: you will need to be able to change matrix map representation for different bases.
Three.V.1, p. 239: 1.6, 1.7 (a,d), 1.9 (b,c), 1.16, 1.18 (a);
Three.V.2, p. 245: 2.10 (a), 2.12 (a,b), 2.13, 2.15, 2.24 (a);
Four.I.1, p. 295: 1.1, 1.3, 1.4 (a), 1.5 (b), 1.8, 1.9, 1.14, 1.16;
Four.I.2, p. 299 (read examples in this section): 2.7, 2.9, 2.11, 2.18, 2.19.

April 5th, 2011, class time.

78

Quiz05 on Thursday, March 31st. (Solution published) Topic: you will need to prove that some map is homomorphism by applying the definition and find a matrix representation of the map.
Three.II.2, p. 190: 2.22 (a,d), 2.23 (a,b), 2.27, 2.34 (a);
Three.III.1, p. 200: 1.11 (a,b,c), 1.12 (b), 1.13, 1.15, 1.17 (a,c), 1.19, 1.21, 1.25 (a,b);
Three.III.2, p. 207: (read corollary 2.5) 2.9 (c), 2.10 (b), 2.13, 2.15, 2.18;
Three.IV.1, p. 212: 1.8 (a,e), 1.14, 1.15, 1.16;
Three.IV.2, p. 218: 2.14 (b,c), 2.16, 2.18, 2.24, 2.30, 2.31;
Three.IV.3, p. 227: 3.23 (a,e), 3.25, 3.27, 3.37, 3.38, 3.39;
Three.IV.4, p. 234: 4.14, 4.15, 4.16 (d,f), 4.17, 4.18, 4.19, 4.20, 4.22, 4.23, 4.29.

March 29th, 2011, class time.



Exam 1 on Thursday, March 3rd. (Solution published) Topics: all covered material.
There will be no homework and quiz this week.
As usual, no calculators or books allowed. You can prepare a page of reference of any formulae etc. you like.
Training set of problems for Exam 1:
One.I.3, p. 29: 3.15 (a,c,e), 3.16 (a,b,d), 3.22;
One.II.1, p. 38: 1.3;
One.II.2, p. 43: 2.13, 2.14, 2.20, 2.25;
One.III.1, p. 51: 1.9 (a,b,d);
One.III.2, p. 120: 2.17;
Two.I.1, p. 86: 1.20 (a,d), 1.21;
Two.I.2, p. 95: 2.28;
Two.II, p. 106: 1.19 (b,d), 1.24;
Two.III.1, p. 114: 1.19, 1.24 (a), 1.26;
Two.III.2, p. 120: 2.16, 2.17, 2.19 (a,d);
Two.III.3, p. 127: 3.19, 3.23;
Three.I.1, p. 164: 1.13 (a,c), 1.31 (a,b,c);
Three.I.2, p. 172: 2.8 (b,c), 2.17 (a,b).

None.

6

Quiz04 on Thursday, February 24th. (Solution published) Topic: Vector Spaces and Linear Systems.
Three.I.1, p. 164: 1.10, 1.13 (a,c), 1.17, 1.19, 1.26 (a,b,c), 1.31 (a,b,c);
Three.I.2, p. 172: 2.8 (b,c), 2.11, 2.17 (a,b);
Three.II.1, p. 179: 1.17 (a,b,c), 1.18 (a,b), 1.19 (a), 1.22, 1.25 (a,b,c), 1.28, 1.31 (a,b).

March 1st, 2011, class time.

5

Quiz03 on Tuesday, February 22nd. (Solution published) Topic: Linear dependence and independence.
Two.III.1, p. 114: 1.16 (a,d), 1.17 (a,b), 1.19 (see p. 111, Example 1.10), 1.20, 1.21 (a,c), 1.23 (a), 1.24 (a), 1.26, 1.27(a), 1.34;
Two.III.2, p. 120: 2.15, 2.16, 2.17, 2.19 (a,d), 2.20, 2.22, 2.23, 2.26, 2.30(a,b);
Two.III.3, p. 127: 3.16 (a,c,e), 3.17 (b), 3.18 (b), 3.19, 3.20 (a,c), 3.21 (a,c,d), 3.23, 3.26, 3.38 (a).

February 22nd, 2011, class time.

4

Quiz02 on Tuesday, February 15th. (Solution published). Topic: GaussJordan reduction.
One.III.1, p. 51: 1.7 (a,d), 1.8 (a,b,c), 1.9 (a,b,d), 1.12;
One.III.2, p. 59: 2.10 (a,b,c,e), 2.17, 2.20, 2.23;
Two.I.1, p. 86: 1.18, 1.19, 1.20 (a,d), 1.21, 1.25, 1.26, 1.27 (b,c,e), 1.29, 1.37;
Two.I.2 (read examples in this section), p. 95: 2.20, 2.21, 2.22, 2.23, 2.24 (a,c,e), 2.26 (a,b,f), 2.27, 2.28, 2.33;
Two.II, p. 106: 1.18 (a,c), 1.19 (b,d), 1.20 (a,b), 1.21(a,f), 1.24, 1.26, 1.32, 1.39.

February 15th, 2011, class time.

23

Quiz02 on Thursday, February 3rd is canceled.
One.I.3, p. 29: 3.15 (a,c,e), 3.16 (a,b,d), 3.18 (a), 3.19, 3.20 (a,c,e), 3.21 (a,d), 3.22;
One.II.1, p. 38: 1.2, 1.3;
One.II.2, p. 43: 2.10 (a,c,e), 2.11, 2.12, 2.13, 2.14, 2.15, 2.20, 2.25, 2.38.

February 8th, 2011, class time.

1

Quiz01 on Thursday, January 27th. (Solution published) Topic: Gauss' method for systems of linear equations.
One.I.1, p. 9: 1.17 (a,b), 1.18 (af), 1.19, 1.20, 1.22, 1.25, 1.28;
One.I.2, p. 18: 2.15, 2.16, 2.18 (a,d,e), 2.19 (a,c), 2.20 (a,b), 2.23, 2.26, 2.27(a), 2.30(a).

January 27th, 2011, class time.

