Matematika Diskrit : Relasi, Sifat Relasi, dan Contoh Soal

Matriks dan Ruang Vektor : Mencari Determinan dengan Metode Baris Tereduksi

Some Theorem About Determinants by Row Reduction

• Let A be a square matrix. If A has a row of zeros or a column of zeros, then det⁡(A) = 0
• Let A be a square matrix. Then det⁡(A) = det⁡(A^T)
• Let A be an n×n matrix:
• If B is the matrix that results when a single row or single column of A is multiplied by a scalar k, then det⁡(B) = k det(A)
• If B is the matrix that results when two rows or two columns of A are interchanged, then det⁡(B) = -det⁡(A)
• If B is the matrix that results when a multiple of one row of A is added to another or when a multiple of one column is added to another, then det⁡(B) = det⁡(A)

Row Operation and Determinant

Using Row Reduction to Evaluate a Determinant

Idea

• Use row reduction to reduce the matrix into triangular matrix
• Calculate the determinant for triangular matrix

If you haven't any ideas to use reduction row matrix, you can check previous article as shown below.

Baca Juga : Matriks dan Ruang Vektor : Gaussian Elimination dan Metode Operasi Baris Elementer Tereduksi ( Reduced Row Echelon Form ) dalam Matriks

Example :

Evaluate det⁡(A) where

Row Operations and Cofactor Expansion

Evaluate det⁡(A) where

Answer :

Sumber

http://informatika.unpar.ac.id/

Slide Materi MRV : Determinants in Matrices