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Chapter 1

Chapter 1. Section 5. Elementary Matrices. An elementary matrix of type I is a matrix obtained by interchanging two rows of I. Elementary Matrices. R ow 1 and Row 2 are switched!. C olumn 1 and Column 2 are switched!. Elementary Matrices.

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Chapter 1

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  1. Chapter 1 Section 5

  2. Elementary Matrices • An elementary matrix of type I is a matrix obtained by interchanging two rows of I

  3. Elementary Matrices Row 1 and Row 2 are switched! Column 1 and Column 2 are switched!

  4. Elementary Matrices • An elementary matrix of type I is a matrix obtained by interchanging two rows of I • An elementary matrix of type II is a matrix obtained by multiplying a row of I by a nonzero constant

  5. Elementary Matrices Row 2 is multiplied by 3! Column 2 is multiplied by 3!

  6. Elementary Matrices • An elementary matrix of type I is a matrix obtained by interchanging two rows of I • An elementary matrix of type II is a matrix obtained by multiplying a row of I by a nonzero constant. • An elementary matrix of type III is a matrix obtained from I by adding a multiple of one row to another row.

  7. Elementary Matrices 4 times Row 3 is added to Row 1 4 times Column 1 is added to column 3

  8. Elementary Row Operations on a Homogenous System R2

  9. Elementary Row Operations on a Homogenous System R2 R3 R3

  10. What happens if there is a zero on the diagonal? R3

  11. R2 R1 R1

  12. Computing the inverse: R1+2R2 R1+R2 R1 R2 R3-5R1 R2/7 R3 R2 25R2+R3 R3

  13. (7/3)R3 R3 R2-(6/7)R3 R2 R1-4R3 R1 R1-5R2 R1

  14. A system is said to be in strict triangular form if, in the kth equation, the coefficients of the first k-1 variables are all zero and the coefficients of the xk is nonzero (k=1,…,n)

  15. Upper Triangular Lower Triangular Diagonal

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