matrix algebra determinant

The determination of all the roots of a given equation is called the solution of the equatio..

Without solving the quadratic equation, the nature of the roots can be determined using the discriminant. i) D >0 i.e., positive and not a perfect square. The roots are real and distinct (irrational). ii) D >0 i.e., perfect square. The roots are rational and distinct. iv) D < 0 i..

Nature of the roots - Without solving the quadratic equation, the nature of the roots can be determined using the discriminant. i) D >0 i.e., positive and not a perfect square. The roots are real and distinct (irrational). ii) D >0 i.e., perfect square. The roots are rational and di..

Ordered Pairs and Cartesian Product - In a Rectangular Cartesian System of coordinates the position of a point in a plane is determined by an ordered pair whose elements give the distances from the intersecting straight lines at right angles to each other. These lines are called the axes...

Let x be the required number. The value of x is determined by solving the equation. Thus \ 2x + x = 36 \ 3x = 36 \ x = 12 \ The number is 12. A man walking at the rate of four kilometres an hour, covers a certain distance in three hours less than another who walks at the rate of three kil..

F = x + y'z A Boolean function is an expression with logical relationship between binary variables. It is evaluated by determining the binary value of the expression for all possible values of the variables..

Different forms of numbers Scientific notation, square roots, exponents, radicals, absolute value, factorial, logarithms Properties of numbers Estimation of solutions Sequences and series Proportionality/direct variation, exponential/fractional expressions Patterns, relations and functions ..

Types of linear systems Gauss-Jordan elimination, Gauss-Jordan method Vectors and vector addition Geometrical solution sets of systems of equations Rectangular matrices to row echelon form Matrix multiplication Inverse to a square matrix Determinants of 2 by 2..

Let A = [aij] be a square matrix. We can associate with the square matrix A, a determinant which is formed by exactly the same array of elements of the matrix A. A determinant formed by the same array of elements of the square matrix..

Determinants - Let A = [a ij ] be a square matrix. We can associate with the square matrix A, a determinant which is formed by exactly the same array of elements of the matrix A. A determinant formed by the same array of elements of the sq..