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 1 = 12 Diagonal 2 = -2

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

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

Area of a Triangle The area of a triangle can be written using the 3 vertices: The ± makes the area always positive. (x1, y1)   (X2, y2) (X3, y3)

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

Cramers Rule for a 2x2 System ax+by=e cx+dy=f The coefficient matrix is A:  

Cramers Rule for a 2x2 System    

Cramers Rule for a 2x2 System    

Cramers Rule for a 3x3 System      

Cramers Rule for a 3x3 System   ax+by+cz=j dx+ey+fz=k gx+hy+iz=l z =  

Cramers Rule for a 3x3 System    

Cramers Rule for a 3x3 System  

Cramers Rule for a 3x3 System  

Cramers Rule for a 3x3 System