Determinants

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Determinants

  1. 1. Warm up <ul><li>Each person solve their problem </li></ul><ul><li>Draw some conclusions about which solutions are equal </li></ul><ul><li>Generalize your conclusions </li></ul>
  2. 2. Sheets Matrices & Geometric Transformations <ul><li>Writing Directions (1 page) </li></ul><ul><li>Direction Master (Transformations 2) (1 page) </li></ul><ul><li>Matrices Transformations 3 (2 page) </li></ul><ul><li>Areas of Transformations (1 page) </li></ul><ul><li>The Shoelace Algorithm (3 page) </li></ul><ul><li>The Mall Problem (2 page) </li></ul><ul><li>Operation Practice (1 page) </li></ul>
  3. 3. Finding the determinant of a matrix <ul><li>The determinate of a matrix is a number associated with the matrix. </li></ul><ul><li>The determinate of matrix A is denoted by | A | </li></ul><ul><li>You can only find the determinate of a square matrix </li></ul>
  4. 4. To find the determinant of a 2 x 2 matrix Example = (3)(2) - (4)(-1) = 6 + 4 = 10 3 -1 4 2
  5. 5. Finding the determinant of a 3 x 3 matrix using “expansion by minors” <ul><li>5 -1 </li></ul><ul><li>-2 0 3 </li></ul><ul><li>1 4 1 </li></ul>= 3 0 3 4 1
  6. 6. Finding the determinant of a 3 x 3 matrix using “expansion by minors” <ul><li>5 -1 </li></ul><ul><li>-2 0 3 </li></ul><ul><li>1 4 1 </li></ul>= 3 0 3 4 1 - 5 -2 3 1 1
  7. 7. Finding the determinant of a 3 x 3 matrix using “expansion by minors” = 3((0)(1)-(4)(3)) – 5((-2)(1)-(1)(3)) +-1((-2)(4)-(1)(0)) = 3(-12) – 5(-5) + -1(-8) = -36+25+8 = -3 <ul><li>5 -1 </li></ul><ul><li>-2 0 3 </li></ul><ul><li>1 4 1 </li></ul>= 3 0 3 4 1 - 5 -2 3 1 1 + -1 -2 0 1 4 Note: Signs!
  8. 8. Finding the determinant of a 3 x 3 matrix using “diagonals” 3 -2 1 5 0 4 = (3 ·0 ·1 + 5 ·3 ·1 + -1 ·-2 ·4) - (-1 ·0 ·1 + 3 ·3 ·4 + 5 ·-2 ·1) = (0+15+8)-(0+36-10) =(23)-(26) = -3 <ul><li>5 -1 </li></ul><ul><li>-2 0 3 </li></ul><ul><li>1 4 1 </li></ul>

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