Presentation on theme: "Matrix Algebra Matrices Matrix Addition and Subtraction Matrix Multiplication Identity and Inverse Matrices Determinant of a Square Matrix Applications."— Presentation transcript:
Matrices Matrix Addition and Subtraction Matrix Multiplication Identity and Inverse Matrices Determinant of a Square Matrix Applications … and why Matrix algebra provides a powerful technique to manipulate large data sets and solve the related problems that are modeled by the matrices.
Each element, or entry, a ij, of the matrix uses double subscript notation. The row subscript is the first subscript i,i, and the column subscript is j.j. The element a ij is the ith row and the jth column. In general, the order of an m × n matrix is m×n.
Refer to text pg 583
An n × n matrix A has an inverse if and only if det A ≠ 0.
Let A, B, and C be matrices whose orders are such that the following sums, differences, and products are defined. 1. Commutative property Addition: A + B = B + A Multiplication: Does not hold in general 2. Associative property Addition: (A + B) + C = A + (B + C) Multiplication: (AB)C = A(BC) 3. Identity property Addition: A + 0 = A Multiplication: A·I n = I n ·A = A
Let A, B, and C be matrices whose orders are such that the following sums, differences, and products are defined. 4. Inverse property Addition: A + (-A) = 0 Multiplication: AA -1 = A -1 A = I n |A|≠0 5. Distributive property Multiplication over addition: A(B + C) = AB + AC (A + B)C = AC + BC Multiplication over subtraction: A(B - C) = AB - AC (A - B)C = AC - BC
Text pg588/589 Exercises #2, 4, 14, 20, 24, and 34