Solving System of Linear Equations using Inverse Matrix (4 Variables)
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What is meant by Linear Equation?
In mathematics, a linear equation is defined as an expression where each term in the variable has an exponent of one. If it is represented in a graph then it results in a straight line. The straight-line equation y=mx+c is an example of a linear equation.
Generally, the form of linear equation is Ax+B=C, where A, B, C are constants and x is variable. Moreover, the linear equations can be written in three distinct ways, they are
- Linear equation in one variable
- Linear equation in two variables
- Linear equation in three variables
Solving the linear equations calculator find the solution of the variable for a given equation within seconds.
Examples of Solving System of Linear Equations using Inverse Matrix (4 Variables)
Question 1: Solve the problem of finding a system of Linear Equations using Inverse Matrix (4 Variables)
78 ๐ฅ1 + 88 ๐ฅ2 + 56 ๐ฅ3 + 8 ๐ฅ4 = 89
2 ๐ฅ1 + 3 ๐ฅ2 + 0 ๐ฅ3 + -1 ๐ฅ4 = -1
-3 ๐ฅ1 + 4 ๐ฅ2 + 1 ๐ฅ3 + 2 ๐ฅ4 = 10
1 ๐ฅ1 + 2 ๐ฅ2 + -1 ๐ฅ3 + 1 ๐ฅ4 = 1
Solution :
As A * A-1 = I
where I is the identity matrix of 4 x 4
Step-1 ----> R2 -> R2 - R1*0.0256
Step-2 ----> R3 -> R3 - R1*-0.0385
Step-3 ----> R4 -> R4 - R1*0.0128
Step-4 ----> R3 -> R3 - R2*9.9309
Step-5 ----> R4 -> R4 - R2*1.1724
Step-6 ----> R4 -> R4 - R3*-0.002
Step-7 ----> R3 -> R3 - R4*6.1045
Step-8 ----> R2 -> R2 - R4*-0.5153
X = A-1. B
Answers
โ x1 = -0.53
โ x2 = 0.9
โ x3 = 1.29
โ x4 = 1.83
FAQs on Solving System of Linear Equations using Inverse Matrix (4 Variables)
1. How do non-linear equations form?
Generally, a non-linear equation is given by ax²+by² = c, where a,b,c are constant values and x, y are variables.
2. How can I Solve a Solving System of Linear Equations using Inverse Matrix (4 Variables) in a fraction of a second?
You can easily & quickly solve a system of Linear Equations using an Inverse Matrix (4 Variables) by using Linearequationscalculator.com offers a free online & handy Linear Equations in Two Variables Calculator.