Overview of Week 2
Math 308M September 30, 2013
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Reading Assignment:
- Read Section 1.3 for Monday, Sept 30.
- Read Section 1.4 for Wednesday, Oct 2.
- 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
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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.
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Vocabulary List:
- Section 1.3:
- the 3 solution possibilities for a linear system of equations
- homogeneous linear systems
- 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:
- This quiz is based on the vocabulary words and homework associated with
Sections 1.2 and 1.3 of the text.
This will be a 10 minute quiz.