Overview of Week 3
Math 308M, October 7, 2013
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Reading Assignment:
- Read Section 1.5 for Monday, Oct 7
- Read Section 1.6 for Wednesday, Oct 9
- Read Section 1.7 for Friday, Oct 11
- Read Section 1.9 for Monday, Oct 14
- Read Section 3.1 for Friday, Oct 18
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Homework Assignment:
- Section 1.2:
Sec. 1.2: 6, 8, 14, 23, 26, 36, 50,
due Oct 2.
- Section 1.3:
Sec. 1.3: 2, 3,
due Oct 2.
- Section 1.3:
Sec. 1.3: 20, 21, 23, 24
Due Oct 9.
- Section 1.4
Sec. 1.4: 2, 6
due Oct 9.
- Section 1.5
Sec. 1.5: 2, 8, 30, 40, 54, 10, 31, 34, 55, 66
due Oct 9.
- Section 1.5
Sec. 1.5: 16, 42, 61(for system i only)
Due Oct 16.
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Vocabulary List:
- Section 1.5:
- equality and sum for matrices
- scalar times a matrix
- n-dimensional vectors and Euclidean n-space
- vector form of general solutions to linear systems
- scalar product of vectors (dot product or inner product)
- matrix vector multiplication
- matrix multiplication
- column block structure of matrix multiplication
- row block structure of matrix multiplication
- Section 1.6:
- the distributive and associative properties for matrix multiplication and addition
- transpose of a matrix
- symmetric matrices
- square matrices
- the identity matrix
- the main diagonal of a matrix
- Euclidean norm (2-norm)
- Section 1.7:
- linear combination of vectors
- zero vector and zero matrix
- linear independence vectors
- standard unit vectors
- nonsingular and singular square matrices
- Theorems 12 and 13
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Key Concepts:
- Section 1.3:
- consistent and inconsistent systems
- homogeneous systems
- An m by n system of linear equations has either (i) no
solution, (ii) infinitely many solutions, or (iii) a unique solution.
- Section 1.5:
- The algebra of matrices: addition, scalar multiplication, and multiplication of matrices
- scalar product of vectors
- row and column block interpretation of marix multiplication
- Section 1.6:
- algebraic properties of matrix algebra
- transpose
- square matrices and special square matrices: identity, zero, symmetric, diagonal
- Euclidean norm
- Section 1.7:
- linear combinations and linear independence
- nonsingular and singular matrices
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Skills to Master:
solving systems by reduction to reduced echelon form
- matrix algebra
- vector representation of the solution set
- checking linear independence
- checking singularity and nonsingularity
- generating linear systems for networks (Sec 1.4)
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Quiz:
Friday, October 11.
- The first question of the quiz will ask your to recite, use, or illustrate
one of the vocabulary words from Sections 1.3, 1.5, and 1.6 listed above.
The second problem will be computational in nature and will be similar to
the homework problems from Sections 1.3, 1.4, and 1.5.