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Table of Contents. 37 . Determinants. Determinants Standard. What is a determinant and how is it used?. A4b Find the inverses of two by two matrices. Essential Question. VOCABULARY. Associated with every square matrix is a whole number called the determinant

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  1. Table of Contents 37. Determinants

  2. DeterminantsStandard What is a determinant and how is it used? A4b Find the inverses of two by two matrices Essential Question

  3. VOCABULARY Associated with every square matrix is a whole number called the determinant The determinant of a Matrix A is denoted by detA or |A|

  4. How to find a determinant of 2x2 = ad - cb

  5. Ex. 1. Evaluate the determinant =1(7) - 4(2) = 7 - 8 = -1

  6. Find the determinant =7(3) - 2(2) = 21 - 4 = 17

  7. Steps for finding determinant of a 3 x 3 matrix Step 1: recopy the first two columns. Step 2: multiply down the diagonals and add the products Step 3: multiply up diagonals and add the products Step 4: Subtract the up diagonal from the down diagonal (down – up)

  8. Ex. 2 Evaluate • -3 • -2 0 • 1 2 (2*0*6 + 4*-2*2) = -3*3*1 + _ (1*0*4 + 6*-2*-3) + 2*3*2 Step 1: recopy the first two columns. = (0 + -9 + -16) – (0 + 12 + 36) Step 2: multiply the down diagonals and add the products. = -25 - 48 Step 3: multiply the up diagonals and add the products NOTE: You subtract the up diagonal from the down diagonal = -73

  9. You try!!! det = -89

  10. Area of a Triangle! • The area of a triangle with vertices (x1,y1), (x2,y2), and (x3,y3) • Area = *Where ± is used to produce a positive area!!

  11. Ex. 3 Find the area of the triangle. Area=

  12. You try!! Find the area of the triangle. Area=

  13. Homework • Pg. 51: #1-9

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