Overview of Week 4
Math 308M, October 14, 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 - 3.3 for Friday, Oct 18
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Homework Assignment:
- 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.
- Sec. 1.6: 2, 12, 29, 42(a, b), 47, 58, 59
4, 10, 25, 26, 28, 41(a), 43, 49
Due Oct 16.
- Sec. 1.7: 6, 8, 21, 22, 30, 40, 48, 50, 52, 53
Due Oct 16.
- Sec. 1.9: 3, 7, 36, 51, 70, 73
10, 16, 17, 22, 34, 40, 53, 69, 79
Due Oct 23,
- Sec. 3.1: 12, 13, 15, 22, 23, 27, 28, 29
Due Oct 23.
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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 of vectors
- linear dependence of vectors
- standard unit vectors
- nonsingular and singular square matrices
- Section 1.9:
- invertible matrices
- inverse of a matrix
- Steps for computing the inverse of a matrix by hand (page 97)
- the formula for inverse of a 2 by 2 matrix (page 98)
- properties of the inverse (Theorem 17 page 99)
- 5 equivalences for nonsingular matrices (Theorem 18 page 101)
- Section 3.2:
- Vector space properties (Theorem 1 page 168)
- verification procedure for showing that a set W is a subspace (page 171, also Theorem 2 page 169)
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Key Concepts:
- 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
- Section 1.9:
- the matrix inverse and its relationship to equation solving
- all of the equivalences to nonsingularity
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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)
- computing the inverse of a matrix
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Quiz:
Friday, October 18.
- The first question of the quiz will ask your to recite, use, or illustrate
one of the vocabulary words from Sections 1.6, 1.7, and 1.9 listed above.
The second problem will be computational in nature and will be similar to
the homework problems from sections 1.5, 1.6, and 1.7.