1. Linear Algebra & Matrices Bachelor Information Technology Dosen Pengampu: Asro Nasiri Drs, M.Kom. STMIK AMIKOM YOGYAKARTA Jl. Ringroad Utara Condong Catur Yogyakarta. Telp. 0274 884201 Fax 0274-884208 Website: www.amikom.ac.id 2. Matrices & vector (1)

2. matrices

3. Or

4. Row Column matrices element matrices m x n If m = n is square matrices

5. Vector Vector : a special matrices that only have one row or one column. Row vector (one row) dan column vector (one column) Contoh :

6. matrices A and B are equal if A and B have the same size and corresponding elements are equal. Vector A and B are equal if A and B have the same dimension and corresponding elements are equal. a = b, u ≠ v, a ≠ u ≠ v and b ≠ u ≠ v

7. matrices can also be referred as collection of vectors  A mxn is matrices A that a collection of m row vector and n column vector.

8. matrices and Vector Operation Addition and substraction of matrices two matrices can added and substrac if have same orde. A + B = C where c ij = a ij + b ij Comutative law : A + B = B + A Associative law : A + (B + C) = (A + B) + C = A + B + C

9. Product of matrices with Scalar λA = B where b ij = λa ij example :

10. matrices Product matrices product of A x B is possible if number of column of A equal the number of rows B. A mxn x B nxp = C mxp

11. Vector multiple of matrices Non vector matrices can be multiple with a column vector, if number of column is same with dimension of column vector. The result is a new column. A mxn x B nx1 = C mx1 n > 1

12. Special matrices Identity matrices : matrices square is if all element in main diagonal is 1, other diagonal are 0.

13. matrices Diagonal matrices diagonal is square matrices that all element is zero except on main diagonal matrices Identitas

14. matrices Null matrices null : matrices that all element are null  0 Contoh :

15. Transpose matrices Row element transpose to column element vice versa A mxn =[a ij ] matrices transpose is  A ′ nxm =[a ji ] (A′) ′ = A

16. matrices Simetrik matrices simetrix if transpose same with its matrices. A = A ′ AA′ = AA = A 2

17. skew symmetric A = -A′ atau A′ = -A

18. inverse matrices If a matrices when multiple of a square matrices resulting a identity matrices A  its inverse is A -1 AA -1 = I A -1 = adj.A  |A|