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Linear Algebra & Matrices Bachelor Information Technology Dosen Pengampu: Asro Nasiri Drs, M.Kom.

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

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Linear Algebra & Matrices Bachelor Information Technology Dosen Pengampu: Asro Nasiri Drs, M.Kom.

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

  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) dancolumn 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  Amxn 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 cij = aij+ bij • 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 bij = λaij • example :

  10. matrices Product • matrices product of A x B is possible if number of column of A equal the number of rows B. • Amxn x Bnxp = Cmxp

  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. • Amxn x Bnx1 = Cmx1 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 • Amxn=[aij] matrices transpose is A′nxm=[aji] (A′) ′ = A

  16. matrices Simetrik • matrices simetrix if transpose same with its matrices. • A = A′ AA′ = AA = A2

  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|

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