Topics include

1. MATRICES

   • concept,

   • notation,

   • order,

   • equality.

   • types of matrices, zero and identity matrices,

   • transpose of a matrix.

   • symmetric and skew-symmetric matrices.

   • Operation on matrices:

   • addition and multiplication, and multiplication with a scalar.

   • simple properties of addition, multiplication, and scalar multiplication.

   • On the commutativity of multiplication of matrices and the existence of non-zero matrices whose product is the zero matrix (restricted to square matrices of order 2). Invertible matrices and proof of the uniqueness of the inverse, if it exists (Here, all matrices will have real entries).

2. DETERMINANTS

determinants of a square matrix (up to 3 x 3 matrices)

minors, co-factors,

applications of determinants in finding the area of a triangle adjoint

the inverse of a square matrix. Consistency, inconsistency, and the number of solutions of systems of linear equations, by example,

solving systems of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.

3. LINEAR Programming

• introduction

• related terminology such as "constraints,"

• objective function, optimization.

• graphical method of solution for problems in two variables,

• feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

  4. PROBABILITY

• conditional probability

• multiplication theorem on probability,

• Independent events, total probability,

• Bayes’ theorem,

• A random variable and its probability distribution,

• the mean of a random variable.

  Topics include

  1. MATRICES

     • concept,

     • notation,

     • order,

     • equality.

     • types of matrices, zero and identity matrices,

     • transpose of a matrix.

     • symmetric and skew-symmetric matrices.

     • Operation on matrices:

     • addition and multiplication, and multiplication with a scalar.

     • simple properties of addition, multiplication, and scalar multiplication.

     • On the commutativity of multiplication of matrices and the existence of non-zero matrices whose product is the zero matrix (restricted to square matrices of order 2). Invertible matrices and proof of the uniqueness of the inverse, if it exists (Here, all matrices will have real entries).

  2. DETERMINANTS

  determinants of a square matrix (up to 3 x 3 matrices)

  minors, co-factors,

  applications of determinants in finding the area of a triangle adjoint

  the inverse of a square matrix. Consistency, inconsistency, and the number of solutions of systems of linear equations, by example,

  solving systems of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.

  3. LINEAR Programming

  • introduction

  • related terminology such as "constraints,"

  • objective function, optimization.

  • graphical method of solution for problems in two variables,

  • feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

    4. PROBABILITY

  • conditional probability

  • multiplication theorem on probability,

  • Independent events, total probability,

  • Bayes’ theorem,

  • A random variable and its probability distribution,

  • the mean of a random variable.