Maricopa Community Colleges  MAT225   19946-19965 
Official Course Description: MCCCD Approval: 04/26/94
MAT225 19946-19965 LEC 3 Credit(s) 3 Period(s)
Elementary Linear Algebra
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 MAT210, or MAT215, or MAT220, or MAT223, or equivalent.
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MCCCD Official Course Competencies:
MAT225   19946-19965 Elementary Linear Algebra
1. 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)
2. Display knowledge of matrix and determinant operations and properties. (I, II)
3. Use the Euclidean inner product and other inner products to define length and distance for vector spaces. (III)
4. Determine whether a set of vectors is a vector space and whether a subser of vectors is a subspace. (III)
5. Determine a basis for a vector space. (III)
6. Use the Gram-Schmidt process to obtain an orthonormal basis for an inner product space. (III)
7. Determine bases for the row space, column space, null space and possible eigenspaces of a matrix A. (III, IV)
8. Determine whether a transformation T is linear and find bases for the kernel and range of T. (V)
9. Use current technology to solve problems in the context of the course. (I, II, III, IV, V)
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MCCCD Official Course Outline:
MAT225   19946-19965 Elementary Linear Algebra
    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 expension
        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 matix
              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
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