10.4 Warm up – No Calc

Section 10.4 – Determinant of a SQUARE Matrix With and Without Calculator By the end of this lesson, you should be able to: Calculate the determinant of a matrix (2x2, 3x3, etc) Identify the notations used for a determinant of a matrix Calculate the MINOR of a matrix

Vocabulary First Determinant – a number (scalar) Notations The 2 x 2 Determinant You can only find the determinant of a square matrix

Try these …

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

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. + – +

– + –

+ – + = 0

Show the initial expansion of the determinant below by using the second row. - +

Show the initial expansion of the determinant below by using the third column. + -

Enter the following matrices into your calculator: Section 10.4– Determinant of a SQUARE Matrix Calculator Required

Using your calculator, compute each of the following: 2 nd Matrix -> 1 2 nd Matrix 1

Right Arrow to see the rest

Clearing the Matrices on the Calculator Now press DEL to delete the matrix marked by the arrow

1. Find the area of the triangle whose vertices are (5, 2), (7, 1), (-2, 3) The area of the triangle is Application 1 – Areas of Plane Figures

2. Find the area of the parallelogram whose vertices are: (2, 6), (1, -3), (-2, 4), (-3, -5) The area of the parallelogram is 34.

3. Use a determinant to determine whether the points (2, 7), (-3, -3), (5, 13) are collinear. Since determinant is zero, the three points are collinear Application 2 – Collinearity of Points

Section 10.4 – Determinant of a SQUARE Matrix With and Without Calculator By the end of this lesson, you should be able to: Calculate the determinant of a matrix (2x2, 3x3, etc) Identify the notations used for a determinant of a matrix Calculate the MINOR of a matrix HOMEWORK: Pg. 751 #9, 11, 16, 19, 22, 31, 34, #62 (parts a-d), #63(parts a-d) 9 total problems, but with the parts a – d it becomes 15 total problems Write all problems out and show your work to receive full credit!