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  • Linear systems and matrices

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  • Matrix equations
  • Linear systems and echelon matrices
  • A linear system is equivalent to a matrix equation.
  • A linear system is equivalent to a vector equation.
  • Terminology
  • Using matrices to solve linear systems
  • Row-equivalent augmented matrices represent equivalent systems

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  • Definition of matrix equation
  • Example of solving a 3-by-3 matrix equation
  • Example of solving a 3-by-3 homogeneous matrix equation
  • A matrix equation is equivalent to a linear system
  • The matrix equation Ax=b has a solution if and only if b is a linear combination of the columns of A.
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  1. Matrix equations

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