Functions, Arithmetic Progression (A.P.), Geometric Progression (G.P.), and Matrix

**Category:** Quantitative Techniques, Research
Methodology

**Author:** Sharma Narender

**Language:** English

**Format:** PDF

**Price:** INR 135.00

Concept of functions, Domain and Range of functions, Types of functions: explicit and implicit functions, single-valued and multivalued functions, increasing and decreasing functions, even and odd functions, polynomial function, rational function, composite function, exponential function, logarithmic function, constant function, identity function, absolute value function, signum function, greatest integer function, reciprocal function. Business applications of functions: Demand function, supply function, total cost function, production function; Cobb-Douglas production function, CES function, revenue function, profit function, consumption function.

Difference between AP and GP, the
magic of GP; the story of the greedy merchant. Arithmetic
Progression; N^{th} term of AP, Sum of ‘n’ terms of AP.
Geometric Progression: N^{th} term of GP, Sum of ‘n’ terms
of GP.

Definition of matrix. Order of matrix. Types of Matrix: Rectangular matrix, square matrix, diagonal matrix, scalar matrix, identity of unit matrix, null matrix or zero matrix, row matrix, column matrix, upper triangular matrix, lower triangular matrix, sub matrix, trace of matrix, equality of two matrix. Matrix operations: Addition and subtraction of matrix, scalar multiplication, properties of matrix addition, matrix multiplication, properties of matrix multiplication. Special types of matrices: Idempotent matrix, nilpotent matrix, involutory matrix, transpose of matrix. Matrix on the basis of transpose: Symmetric matrix, Skew symmetric matrix, orthogonal matrix. Determinants: Determinants of order one, two and three, Minors and Co-factors, properties of determinants. Adjoint of square matrix. Inverse of square matrix. Simultaneous linear equations: Cramer’s Rule, Inverse method. Economic applications of matrix.