MATRICES

Presented By,

Neelam H. WadhwaniAmruta D. Shriraotqma2z.blogspot.com

WHAT IS MEANT BY MATRIX?

A matrix is an ordered rectangular array of numbers or functions. The numbers or functions are called the elements or the entries of the matrix.

TYPES OF MATRICES

1. RECTANGULAR MATRIX2. SQUARE MATRIX3. ROW AND COLUMN MATRIX4. DIAGONAL MATRIX5. SCALAR MATRIX6. UNIT MATRIX7. ZERO MATRIX

OPERATION OF MATRICES

1. EQUALITY OF MATRICES2. ADDITION OF MATRICES3. SUBTRACTING OF MATRICES4. MULTIPLICATION OF MATRICES

1. EQUALITY OF MATRICES: Two matrices are said to be equal if they have the same order and all the corresponding elements are equal.

2. ADDITION OF MATRICES: The sum of two matrices of the same order is the matrix whose element are the sum of the corresponding elements of the given matrices.

3. SUBTRACTING OF MATRICES: Subtraction of the matrices is also done in the same manner of addition of matrices. When the matrix B is to be subtracted from matrix A, the elements in a matrix B are subtracted from corresponding elements in matrix A.

4. MULTIPLICATION OF MATRICES: A matrix may be multiplied by any number or any other matrix. Multiplication of a matrix by any one number is called a scalar multiplication.

PROPERTIES OF MATRIX MULTIPLICATION1. Matrix multiplication is associative: If A, B

and C are three matrices, and AB, BC are defined then

A(BC)=(AB)C

2. Matrix multiplication is distributive: If A, B and C are three matrices of proper order then

A(B+C)=AB+AC and (B+C)A=BA+CA

3. Matrix multiplication is in general, not commutative: If A & B are two matrices such that AB and BA are defined, then AB is not equal to BA in general.

TRANSPOSE OF A MATRIX

The matrix obtained by interchanging the rows and columns of a matrix is called transpose of a matrix. The transpose of a matrix A is denoted by A’.