Ch. 3: Determinant of a Matrix

What is the pattern that can be used to find the determinant of a 4X4 or higher matrix? What's the name for the method?

Pattern (called "Laplace Expansion") 1. Plus a (a_11) times the determinant of the matrix that is not in a's row or column. 2. Minus b (a_12) times the determinant of the matrix that is not in b's row or column. 3. Plus c (a_13) times the determinant of the matrix that is not in c's row or column. 4. Minus d (a_14) times the determinant of the matrix that is not in d's row or column.

What is the determinant of a matrix? Symbol?

a special number that can be calculated from a square matrix - Helps us find the inverse of a matrix (used in inverse calculation) - Useful in systems of linear equations and calculus Symbol: see image - Same symbol as absolute value

What requirement must be met to calculate a determinant?

the matrix must be a square matrix

What is the general technique that is used to solve for the determinant of a 3X3 matrix?

1. Multiply element a (a_11) by the determinant of the 2X2 matrix that is not in a's row or column. 2. Do the same process for b (a_12) and c (a_13). 3. Sum the result. Note: b (a_12) is negative

What is a singular matrix?

A matrix with a determinant that equals zero or one that does not have an inverse.