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Official Course
Description: MCCCD Approval: 6-27-1995 |
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MAT225
1996 Fall – 1998 Summer II |
LEC 3.0
Credit(s) 3.0 Period(s) 3.0 Load Acad |
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Elementary
Linear Algebra |
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Introduction to matrices, systems of linear equations,
determinants, vector spaces, linear transformations and eigenvalues.
Emphasizes the development of computational skills. Prerequisites: Grade of "C" or
better in MAT212 or MAT220, or MAT221, or equivalent. |
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Go to Competencies Go to Outline
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MCCCD
Official Course Competencies: |
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MAT225 1996
Fall – 1998 Summer II |
Elementary Linear Algebra |
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1.
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Analyze the
existence and character of the solution(s) of a system of linear equations
using a rowechelon form of the augmented matrix
determinant. (I, II) |
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2.
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Display knowledge of matrix and determinant operations and
properties. (I, II) |
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3.
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Use the Euclidean inner product and other inner products
to define length and distance for vector spaces. (III) |
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4.
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Determine whether a set of vectors is a vector space and
whether a subset of vectors is a subspace. (III) |
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5.
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Determine a basis for a vector space. (III) |
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6.
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Use the Gram-Schmidt process to obtain an orthonormal basis for an inner product space. (III) |
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7.
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Determine bases for the row space, column space, null
space and possible eigenspaces of a matrix A. (III,
IV) |
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8.
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Determine whether a transformation T is linear and find
bases for the kernel and range of T. (V) |
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9.
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Use current technology to solve problems in the context of
the course. (I, II, III, IV, V) |
Go to Description Go to top of
Competencies
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MCCCD
Official Course Outline: |
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MAT225 1996
Fall – 1998 Summer II |
Elementary Linear Algebra |
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I. Linear Equations and
Matrices A. Linear Systems 1. Methods of elimination 2. Dependent and
inconsistent systems B. Matrices 1. Operations on matrices 2. Properties of matrix
operations 3. Inverse of a matrix 4. Solutions of equations
using matrices II. Determinants A. Definitions and
properties B. Cofactor expansion III. Vectors and Vector
Spaces A. Vectors in R2 and R3 1. Vector operations 2. Orthogonal and unit
vectors B. Vectors in Rn 1. Inner product 2. Triangle inequality C. Vector spaces and
subspaces 1. Properties of vector
spaces 2. Definition of a subspace
3. Span of a set of vectors
D. Linear independence E. Basis and dimension 1. Definition of a basis 2. Finite and infinite -
dimensional vector spaces F. Rank of a matrix 1. Row rank and column rank
2. Consistency of non
homogeneous linear systems G. Orthonormal
basis in Rn (Gram-Schmidt process) IV. Eigenvalues
and Eigenvectors A. Characteristic
polynomials and equations for square matrices B. Determining eigenvalues and eigenvectors for a square matrix C. Diagonalization
of a matrix V. Linear Transformations
and Matrices A. Properties and examples
of linear transformations B. Kernel and range of a
linear transformation C. Matrix of a linear
transformation |