Matrix and Determinant Operations
<ul><li>MATRIX:   A rectangular arrangement of numbers in rows and columns. </li></ul><ul><li>The  ORDER  of a matrix is t...
A matrix is any doubly subscripted array of elements arranged in rows and columns.
What is the order? 3 x 3 3 x 5 2 x 2  4 x 1 1 x 4 (or square matrix) (Also called a row matrix) (or square matrix) (Also c...
Row Vector [1 x n] matrix  
Column Vector [m x 1] matrix
Identity Matrix Square matrix with ones on the diagonal and zeros elsewhere.
Transpose Matrix Rows become columns and columns become rows
<ul><li>To add two matrices, they must have the same order.  To add, you simply add corresponding entries. </li></ul>Addin...
= = 7 7 4 5 0 7 5 7
Subtracting Two Matrices <ul><li>To subtract two matrices, they must have the same order.  You simply subtract correspondi...
= 5-2 -4-1 3-8 8-3 0-(-1) -7-1 1-(-4) 2-0 0-7 = 2 -5 -5 5 1 -8 5 3 -7
<ul><li>In matrix algebra, a real number is often called a  SCALAR .  To multiply a matrix by a scalar, you multiply each ...
-2 6 -3 3 -2(-3) -5 -2(6) -2(-5) -2(3) 6 -6 -12 10
Matrix Multiplication Matrices A and B have these dimensions: [r x c] and [s x d]
Matrix Multiplication Matrices A and B can be multiplied if: [r x  c ] and [ s   x d] c = s
Matrix Multiplication The resulting matrix will have the dimensions: [ r  x c] and [s x  d ] r x d
Multiplying Two Matrices
<ul><li>We can only find the determinant of a square matrix </li></ul><ul><li>The value of the determinant for a 2×2 matri...
Determinants of a three  by three  cross matrix
Matrix Operations in Excel Select the cells in which the answer will appear
Matrix Multiplication in Excel <ul><li>Enter “=mmult(“ </li></ul><ul><li>Select the cells of the first matrix </li></ul><u...
Matrix Multiplication in Excel Enter these three key strokes at the same time: control  shift  enter
Multiplying Two Matrices using Excel
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Ses 2 matrix opt

  1. 1. Matrix and Determinant Operations
  2. 2. <ul><li>MATRIX: A rectangular arrangement of numbers in rows and columns. </li></ul><ul><li>The ORDER of a matrix is the number of the rows and columns. </li></ul><ul><li>The ENTRIES are the numbers in the matrix. </li></ul>What is a Matrix? rows columns <ul><li>This order of this matrix is a 2 x 3. </li></ul>
  3. 3. A matrix is any doubly subscripted array of elements arranged in rows and columns.
  4. 4. What is the order? 3 x 3 3 x 5 2 x 2 4 x 1 1 x 4 (or square matrix) (Also called a row matrix) (or square matrix) (Also called a column matrix)
  5. 5. Row Vector [1 x n] matrix  
  6. 6. Column Vector [m x 1] matrix
  7. 7. Identity Matrix Square matrix with ones on the diagonal and zeros elsewhere.
  8. 8. Transpose Matrix Rows become columns and columns become rows
  9. 9. <ul><li>To add two matrices, they must have the same order. To add, you simply add corresponding entries. </li></ul>Adding Two Matrices
  10. 10. = = 7 7 4 5 0 7 5 7
  11. 11. Subtracting Two Matrices <ul><li>To subtract two matrices, they must have the same order. You simply subtract corresponding entries. </li></ul>
  12. 12. = 5-2 -4-1 3-8 8-3 0-(-1) -7-1 1-(-4) 2-0 0-7 = 2 -5 -5 5 1 -8 5 3 -7
  13. 13. <ul><li>In matrix algebra, a real number is often called a SCALAR . To multiply a matrix by a scalar, you multiply each entry in the matrix by that scalar. </li></ul>Multiplying a Matrix by a Scalar
  14. 14. -2 6 -3 3 -2(-3) -5 -2(6) -2(-5) -2(3) 6 -6 -12 10
  15. 15. Matrix Multiplication Matrices A and B have these dimensions: [r x c] and [s x d]
  16. 16. Matrix Multiplication Matrices A and B can be multiplied if: [r x c ] and [ s x d] c = s
  17. 17. Matrix Multiplication The resulting matrix will have the dimensions: [ r x c] and [s x d ] r x d
  18. 18. Multiplying Two Matrices
  19. 19. <ul><li>We can only find the determinant of a square matrix </li></ul><ul><li>The value of the determinant for a 2×2 matrix is: det A = m11 m22 - m12 m 21 </li></ul>What is a Determinant? rows columns <ul><li>Find the determinant value of the matrix </li></ul>
  20. 20. Determinants of a three by three cross matrix
  21. 21. Matrix Operations in Excel Select the cells in which the answer will appear
  22. 22. Matrix Multiplication in Excel <ul><li>Enter “=mmult(“ </li></ul><ul><li>Select the cells of the first matrix </li></ul><ul><li>Enter comma “,” </li></ul><ul><li>Select the cells of the second matrix </li></ul><ul><li>Enter “)” </li></ul>
  23. 23. Matrix Multiplication in Excel Enter these three key strokes at the same time: control shift enter
  24. 24. Multiplying Two Matrices using Excel
  25. 25. Thank you
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