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