Systems of Linear Equations

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Systems of Linear Equations

• System of linear equations
• No solution set
• Exactly one solution
• Infinitely many solutions

System of linear equations Solution
set Equivalent systems
Consistent at least 1 solution or
many Inconsistent no solutions
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Systems of Linear Equations
Solving linear systems
Use a rectangular array called a matrix.

• Elementary row operations
• Replace a row by the sum of itself and a multiple
  of another row. replacement
• Interchange two rows. Interchange.
• Multiply all entries in a row by a nonzero
  constant. Scaling.

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Systems of Linear Equations
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Systems of Linear Equations
Example of inconsistent system
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Systems of Linear Equations
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Systems of Linear Equations
Linear equation
TI Project Echelon Forms
coefficients
Learn to use/do the following Matrix
creation rowswap row row ref rref
Solution set
Coefficient matrix
Augmented matrix