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Linear System of Simultaneous Equations Warm UP

Linear System of Simultaneous Equations Warm UP. First precinct: 6 arrests last week equally divided between felonies and misdemeanors. Second precinct: 9 arrests - there were twice as many felonies as the first precinct.

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Linear System of Simultaneous Equations Warm UP

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  1. Linear System of Simultaneous Equations Warm UP First precinct: 6 arrests last week equally divided between felonies and misdemeanors. Second precinct: 9 arrests - there were twice as many felonies as the first precinct. Write a system of two equations and find out how many felonies and misdemeanors occurred.

  2. Sections 4.1 & 4.2 Matrix Properties and Operations

  3. Algebra

  4. Matrix A matrix is any doubly subscripted array of elements arranged in rows and columns enclosed by brackets. Element

  5. Dimensions of a Matrix 3, 2

  6. Name the Dimensions

  7. Row Matrix [1 x n] matrix

  8. Column Matrix [m x 1] matrix

  9. Square Matrix Same number of rows and columns Matrices of nth order -B is a 3rd order matrix

  10. The Identity

  11. Identity Matrix Square matrix with ones on the diagonal and zeros elsewhere.

  12. The Equal

  13. Equal Matrices Two matrices are considered equal if they have the same dimensions and if each element of one matrix is equal to the corresponding element of the other matrix. = Can be used to find values when elements of an equal matrices are algebraic expressions

  14. To solve an equation with matrices • 1. Write equations from matrix • 2. Solve system of equations • Examples • = • =

  15. Linear System of Simultaneous Equations How can we convert this to a matrix?

  16. Matrix Addition A new matrix C may be defined as the additive combination of matrices A and B where: C = A + B  is defined by: Note: all three matrices are of the same dimension

  17. Addition If and then

  18. Matrix Subtraction C = A - B Is defined by

  19. Subtraction If and then

  20. Matrix Addition Example

  21. Multiplying Matrices by Scalars

  22. Matrix Operations

  23. Matrix Multiplication Matrices A and B have these dimensions: Video [r x c] and [s x d]

  24. Matrix Multiplication Matrices A and B can be multiplied if: [r x c] and [s x d] c = s

  25. Matrix Multiplication The resulting matrix will have the dimensions: [r x c] and [s x d] r x d

  26. A x B = C [2 x 2] [2 x 3] [2 x 3]

  27. A x B = C [3 x 2] [2 x 3] Result is 3 x 3 [3 x 2] [2 x 3] A and B can be multiplied [3 x 3]

  28. Inversion

  29. Matrix Inversion Like a reciprocal in scalar math Like the number one in scalar math

  30. Transpose Matrix Rows become columns and columns become rows

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