LINEAR SIMULTANEOUS EQUATIONS (Sarala Saha Samikarana Question Answer) Definition and Basics:
Sarala Saha Samikarana chapter 1 All Question Answer of Exercise 1(a),Exercise 1(b) and Exercise 1(c) are avaiable for odiamedium students.
Linear simultaneous equations involve two or more linear equations with multiple variables. The primary goal is to find the values of these variables that satisfy all the equations simultaneously. The equations are ‘linear’ because the highest power of the variables is 1, and ‘simultaneous’ because the solution must satisfy all equations at the same time.
The general form of a system of linear simultaneous equations with n variables is:
a₁₁x₁ + a₁₂x₂ + … + a₁nxₙ = b₁ a₂₁x₁ + a₂₂x₂ + … + a₂nxₙ = b₂ . . . aₘ₁x₁ + aₘ₂x₂ + … + aₘnxₙ = bₘ
Here, aᵢⱼ represents coefficients, xᵢ are the variables, and bᵢ are constants.
Chapter 1 LINEAR SIMULTANEOUS EQUATIONS Exercise 1(a)
Chapter 1 LINEAR SIMULTANEOUS EQUATIONS Exercise 1(b)
Chapter 1 LINEAR SIMULTANEOUS EQUATIONS Exercise 1(c)
Sarala Saha Samikarana Question Answer Exercise 1(a)
Sarala Saha Samikarana Question Answer Exercise 1(b)
Sarala Saha Samikarana Question Answer Exercise 1(c)
- Geometric Interpretation:
Linear simultaneous equations can be visualized geometrically using the concept of lines in a coordinate plane. Each equation represents a line, and the intersection point of these lines, if it exists, is the solution to the system. The number of equations determines the dimensionality of the problem: two equations represent lines, three represent planes, and so on.
- Methods of Solving:
Several methods are available to solve linear simultaneous equations:
a. Substitution Method: Solve one equation for one variable and substitute this expression into the other equations.
b. Elimination Method: Manipulate the equations to eliminate one variable, making it easier to solve for the remaining variables.
c. Matrix Method: Represent the system of equations in matrix form and use techniques like Gaussian elimination or matrix inversion.
d. Cramer’s Rule: Applicable when the system has the same number of equations and variables. It expresses the solution using determinants.
Chapter 1 LINEAR SIMULTANEOUS EQUATIONS Exercise 1(a)
Chapter 1 LINEAR SIMULTANEOUS EQUATIONS Exercise 1(b)
Chapter 1 LINEAR SIMULTANEOUS EQUATIONS Exercise 1(c)