matrix algebra tutorial 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..

If f and g are two functions defined over same domain D, then we have certain set of identities which can be used for solving limits problems with variables like algebraic expression..

Fundamentals of Equations Algebraic and transcendental equations; If f(x) is a polynomial in x, then f(x) =0 is an algebraic equation. Example; x 7 + 5x - 2=0. If f(x) contains algebraic and non algebraic functions namely exponential, logarithmic, t..

A solution of a linear equation is the value of the variable which makes LHS = RHS. It is also called the "root" of the equation. To solve a linear equation , we transpose all the terms containing the variable to one side and the constant terms to the other. The equation then reduces to th..

A linear equations in two variables x and y is of the form ax + by + c = 0 ( ) where a, b, c are real numbers. To find a solution for this equation, we can assign any value for one of the variables and find the value of the other variable such that the two sides of the equation are equal. Henc..

Linear equations in two variables - A Linear equation is a first degree algebraic expression with one,two or more variables equated to a constant. Graphically a linear equation with one or two variables is a straight line whereas one with three variable represents a plane. A simple linear..