| Chapter.Section | Problems for quizz |
Problems Due |
Due date |
| 1.1 1.2 |
2, 3ab, 4a-d, 5b, 6a, 10 |
same | 8/25 |
| A) Show that AkB = kAB B) Show associativity of multiplication with a general 2x2 |
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| 1.3 | 1, 2, 4e, 6ab, 12, 14a | same | 9/3 |
A) Complete the definition of Matrix Multiplication with notation given in class. B) Show that C) Estimate the temperatures T1,T2,T3,T4 by constructing a system of equations by using the given information in the Temperature Distribution hand-out, then solving the system by performing Gauss-Jordan elimination on the augmented matrix reresenting the system. |
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| 1.4 | 4a, 9, 11, 12, 14, 20, 21, 31, 17 | same | 9/8 |
| 1.5 | 1, 2, 3ab, 5a, 6a, 7e, 11, 15, 18 | same | 9/15 |
| 1.6 | 7, 8, 16, 17, 23, 28 | Not to be turned in, but just to make sure you understand and know how to do the problems. |
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| 1.7 | 1a, 3b, 4, 5, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26 | ||
| 2.1 | 1, 2b, 3d, 13, 22, 24, 25 | 10/1 |
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| 2.2 | 2ac, 3, 5 | ||
| 2.4 | 3, 4, 7, 11, 12, 13, 14, 20 | ||
| 2.3 | 2, 12, 15, 16 | 10/6 |
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| 3.1 | 1cg, 2b, 3be, 5, 6a, 8, 9, 11,12,17 | ||
| A) | Given the matrix A (given in class), show that det A gives the area of the parallelogram determined by the row vectors of A. |
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| B) | Given the matrices B and C in class, show linearity of the determinant function using the defined scalar multiple and row addition. | ||
| 3.3 | 1ac, 2ac, 3a, 16ac | ||
| 6.1 | 1, 4 | ||
9-20
Know every definition, and the proofs for the following, for Exam 1.
1. Show that if AB and BA are both defined, then AB and BA are square matrices.
2. Show that if a square matrix A satisfies AA - 3A + I = 0, then A-inverse = 3I - A.
3. Let A and B be square matrices such that AB = 0. Show that if A is invertible, then B = 0.
4. A square matrix A is called symmetric if A-transpose = A and skew-symmetric if A-transpose = -A.
Show that if B is a square matrix, then B - B-transpose is skew-symmetric.
5. Prove that if A is an invertible skew-symmetric matrix, then A-inverse is skew-symmetric.
6. Show that the transpose of A-transpose = A.
7. Show that A(B + C) = AB + AC.
8. Show that if B and C are inverses of a matrix A, then B = C.
9. If A and B are both non-singular nxn matrices, then AB is non-singular and (AB)-inverse = (B-inverse)x(A-inverse).
10. If A is a non-singular matrix, then A-transpose is non-singular and (A-inverse)-transpose = (A-transpose)-inverse.
11. Given an nxn matrix A, such that A is invertible, then Ax = b has exactly one solution for every nx1 matrix b.