Algebra Practice Test
This course covers topics such as matrices, determinants, linear programming, and probability. It is suitable for beginners and provides a comprehensive introduction to these concepts. Learn about matrix operations, solving linear equations, and probability theory. Gain a solid foundation in these fundamental mathematical concepts.
Topics include
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).
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
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).
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.
Who this course is for:
- beginner
