PROPERTIES OF MATRICES

like its matrix representation to be simple, diagonal if possible We therefore need some way of deciding if we can simplify the matrix representation and then how to do so This problem has a solution, and in order to implement it, we need to talk about something called the determinant of a matrix The determinant of a square matrix is a number

Lineer Cebir (Matris – Determinant)

(3x3) (3x2) (3x2) 1 satırx1 sütun 11 1 satırx2 sütun 12 2 satırx1 sütun 21 2 satırx2 sütun 22 3 satırx1 sütun 31 ax by cz at bu cv Determinant

CHAPTER 25: WORKING WITH MATRICES

3x2 Array Origin: MathCAD refers to the first If the determinant of the coefficient matrix is nonzero, then the system has a unique solution 2x 1 + 3x

PROPERTIES OF MATRICES

x1 + 3x2 − x3 = 7 x1 + x2 + x3 =1 We express them in matrix form: = − 1 7 3 1 1 1 1 3 1 2 1 1 3 2 1 x x x Where matrix A is = − 1 1 1 1 3 1 2 1 1 A and vector y is 1 7 3 According to Cramer’s rule: 1 3 1 1 7 3 1 1 1 1 8 2 4 x A − = = = To find x1 we replace the first column of A with vector y and divide the determinant of this new

Chapter 9

matrix or a column vector 2 Null or Zero Matrix: A matrix in which each element is „0‟ is called a Null or Zero matrix Zero matrices are generally denoted by the symbol O This distinguishes zero matrix from the real number 0 For example O = 0000 0000 ªº «» ¬¼ is a zero matrix of order 2 x 4 The matrix O mxn

Topic 3: MATRICES

To find inverse of 3 X 3 matrix, First need to calculate determinant A = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ 33 23 32 22 31 21 11 12 13 a a a a a a a a a Corresponding to each aij is a co-factor Cij 9 elements in 3X3 ⇒ 9 co-factors Co-factor Cij = determinant of 2X2 matrix obtained by deleting row i and column j of A, prefixed by + or

Les déterminants de matricesANG - HEC Montréal

The minor / 5 6 is the determinant of the matrix obtained by eliminating the first row and the second column of #, i e / 5 6 L Z 53 83 Z L5 3 F3 8 L15 F24 L9 The minor / 6 6 is the determinant of the matrix obtained by eliminating the second row and the second column of #, i e / 6 6 L Z 24 83 Z L2 3 F4 8 L6 F32 L

4 Matrix Operations in Excel Matrix Manipulations: Vectors

The mathematical operation of “transposing” a matrix is simply to switch the “rows” with the “columns” Hence, a row vector’s transpose is a column vector and the transpose of a 2x3 matrix is a 3x2 matrix To take the transpose of a matrix, use the TRANSPOSE function Inverting A Matrices

Matrix & Vector - Stony Brook

If A is a mxr matrix and B is a rxn matrix, then the product C=AB is a mxn matrix whose entries are obtained as follows The entry corresponding to row ‘i’ and column ‘j’ of C is the dot product of the vectors formed by the row ‘i’ of A and column ‘j’ of B 3x3 3x2 3x2 1 2 4 1 3 A 3 0 7 B 3 1 9 1 5 1 0 3 5 1 1 C AB 10 9 notice 2 3 3

[PDF] PROPERTIES OF MATRICES

Determinants - Texas A&M University

Lineer Cebir (Matris – Determinant)

CHAPTER 25: WORKING WITH MATRICES

PROPERTIES OF MATRICES

Chapter 9

Topic 3: MATRICES

Les déterminants de matricesANG - HEC Montréal

4 Matrix Operations in Excel Matrix Manipulations: Vectors

Matrix & Vector - Stony Brook