Previously, you learned about deriving an augmented matrix from a system of linear equations. You have also learned about reducing the augmented matrix into a simpler equivalent matrix that is easy to solve through series of row operations on the matrix. This kind of matrix form is known as the row echelon form of matrix. … Read more
Earlier we learnt that we can solve for unknown variables by substituting arbitrary values for the equation. You can by solving for or one at a time. Now, a system of equations have equations which we change into a new system having same solution set but simplified and easy to solve. This is achieved by … Read more
In the previous article, we learned about systems of linear equations can be represented using a matrix or augmented matrix. There are many types of matrices which we are going to explore in this post. In general matrix are referred using their order which is where is the rows and is number of columns in … Read more
Some linear systems have no solution; they are called inconsistent systems. If a linear system has at least one solution than it is called consistent system. To illustrate this with example, consider two linear equations that represents two line on xy-plane given below. where either one variable can be zero, not both. Let us call … Read more
Before you we try to understand the system of linear equations, we must understand the basic terminologies that we are going to use in the linear algebra. Linear Equations Linear equation represents a straight line on a xy-plane or co-ordinate plane. Therefore, linear equation in n variable is given as where $a_{1}, a_{2}, a_{3} \hspace{1ex}$ … Read more
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