MATRICES MATRIX OPERATIONS Matrix Determinants A Determinant is

MATRICES MATRIX OPERATIONS

Matrix Determinants § A Determinant is a real number associated with a matrix. Only SQUARE matrices have a determinant. § The symbol for a determinant can be the phrase “det” in front of a matrix variable, det(A); or vertical bars around a matrix, |A| or.

Matrix Determinants To find the determinant of a 2 x 2 matrix, multiply diagonal #1 and subtract the product of diagonal #2. Diagonal 2 = -2 Diagonal 1 = 12

Matrix Determinants To find the determinant of a 3 x 3 matrix, first recopy the first two columns. Then do 6 diagonal products. 18 60 16 -20 -24 36

Matrix Determinants The determinant of the matrix is the sum of the downwards products minus the sum of the upwards products. 18 60 16 = (-8) - (94) = -102 -20 -24 36

Area of a Triangle n The area of a triangle can be written using the 3 vertices: (x 1, y 1) (X 3, y 3) n (X 2, y 2) The ± makes the area always positive.

(2, 7) Example (-2, -1) (6, 1) - 8 (-56) = 28 sq. units

Cramers Rule for a 2 x 2 System ax+by=e cx+dy=f n The coefficient matrix is A:

Cramers Rule for a 2 x 2 System n

Cramers Rule for a 2 x 2 System n

Cramers Rule for a 3 x 3 System n

Cramers Rule for a 3 x 3 System ax+by+cz=j dx+ey+fz=k gx+hy+iz=l n z=

Cramers Rule for a 3 x 3 System n

Cramers Rule for a 3 x 3 System n

Cramers Rule for a 3 x 3 System n

Cramers Rule for a 3 x 3 System n