1. Section 4.3 – A Review of Determinants Section 4.4 – The Cross Product

2. Vocabulary First (Again ) Determinant – a number (scalar) Notations The 2 x 2 Determinant

3. Try these four… …and these four

4. The MINOR of a matrix 1.Cross out the row and column of the element 2.Compute the determinant of what remains

5. The 3 x 3 Determinant 1. Select ANY row or column (most zeros would be smart) 2. Take each element and multiply it by its MINOR. 3.Apply + - + - + - (to be explained). Remember the + starts with the first row first column element. + – +

6. – + –

7. + – + = 0

8. Definition The cross product of two vector yields a vector which Is orthogonal to the two given vectors. If A = ai + bj + ck and B = di + ej + fk

9. Find the vector orthogonal to A = 2i + 3j + k and B = 3i - 2j + 5k

10. Find the vector orthogonal to A = 7i + 1j + 2k and B = i + 3j + 4k