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This section describe thematrix algebra, especiallymultiplication.Matrices

MatrixDefinition: A rectangular arrangement of number in rows and columns

Generalized form of a MatrixA matrix A Containing elements aij has the general form A =

Different types of MatricesColumn Matrix: A vertical set of numbers in a matrix Example: A = Row Matrix : A horizontal set of numbers in a matrixExample: A = [3 9 6]

Different types of MatricesSquare Matrix - A matrix that has the equal numbers of rows and columnsExampleA = A =

Different types of MatricesIdentity Matrix or Unit Matrix: An identity matrix is a diagonal matrix in which the diagonal elements are equal to 1. A =

Different types of MatricesZero MatricesEvery element of a matrix is zero, it is called a zero matrix, i.e., A =

Different types of MatricesScalar MatrixA scalar matrix is a diagonal matrix in which the diagonal elements are equal. A =

Dimensions of MatrixNumber of rows by number of columns of a matrix.Written in the form rows columnsExamples: Find the dimensions of each matrix.

Dimensions: 3x2Dimensions: 4x1Dimensions: 2x4Transpose of a matrixDEFINITIONLet A be an (m n) matrix. Then at the transpose of A is the matrix obtained by interchanging the rows and columns of A.Transpose of A denoted by At is an (n m) matrixTranspose of a Matrix

Matrix Operations1. Addition of Matrix2. Subtraction of Matrix3. Multiplication of Matrix

Addition of MatricesIf A and B are both m n matrices then the sum of A and B, denoted A + B, is a matrix obtained by adding corresponding elements of A and B.

If A and B are both m n matrices then the sum of A and B, denoted A + B, is a matrix obtained by adding corresponding elements of A and B. add these

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add theseTo add two matrices, they must have the same order. To add, you simply add corresponding entries.

Addition of Matrices

Subtraction of Matrices

To subtract two matrices, they must have the same order. You simply subtract corresponding entries.Scalar multiplication of matrixIn matrix algebra, a real number is often called a SCALAR. To multiply a matrix by a scalar, you multiply each entry in the matrix by that scalar.

Multiplying Matrices

Dimensions: 3 x 22 x 3They must match.The dimensions of your answer.Order of MatrixThe number of columns in first matrix must equal number of rows in second matrix. Row x Columns = Row x Columns

3 x 2 3 x 2NO2 x 3 3 x 2YES3 x 2 2 x 3YES3 x 1 1 x 3YES2 x 2 2 x 2YES3 x 3 2 x 2NOFollowing Matrix possible ?22What is the dimension of the following products, if possible?

3 x 2 3 x 2NO2 x 3 3 x 2YES3 x 2 2 x 3YES3 x 1 1 x 3YES2 x 2 2 x 2YES3 x 3 2 x 2NO2 x 23 x 33 x 32 x 223