Learn what an independent system of equations is and what a consistent and independent system looks like on a graph. Find examples of independent...
A system of equations [A][X]=[B][A][X]=[B] is consistent if the rank of AA is equal to the rank of the augmented matrix [A|B][A|B]. A system of equations [A][X]=[B][A][X]=[B] is inconsistent if the rank of AA is less than the rank of the augmented matrix [A|...
A system of equations [A][X]=[B][A][X]=[B] is consistent if the rank of AA is equal to the rank of the augmented matrix [A|B][A|B]. A system of equations [A][X]=[B][A][X]=[B] is inconsistent if the rank of AA is less than the rank of the augmented matrix [A|...
Learn the system of equations definition. Discover the different types of systems of equations and learn about the solutions, as well as solution...
To solve the problem, we need to determine the value of|α|for which the given system of equations has no solutions. The system of equations is: 1.αx+y+z=α−1 2.x+αy+z=α−1 3.x+y+αz=α−1 Step 1: Write the system in matrix form ...
To determine the condition under which the given system of equations has a non-trivial solution, we need to analyze the coefficient matrix and its determinant. The system of equations is as follows:1. \( x + y + z = 0 \) 2. \( ax + by + z = 0 \
System of linear equations can arise naturally from many real life examples. Generally speaking, those problems come up when there are two unknowns or variables to solve. In the figure above, there are two variables to solve and they are x and y. This kind of system is called system of ...
Property 1: If A is a square matrix (i.e. the number of equations is equal to the number of unknowns), the equation AX = C has a unique solution if and only if A is invertible (i.e. det A≠ 0), and in this case, the unique solution is given by X = A–1C. Proof: Supp...
From the solution of the heat and mass diffusion equations that describe the exothermic physical absorption of a gas into a liquid, compact formulae for the sums of two infinite series are derived. The method is general and should be applicable to other systems of linear, parabolic partial ...
With the aid of the operations depicted in Section 3.2.1, the above formula takes the following form: 𝑅=∑𝑗=1𝑛𝐾𝑗(𝜇𝑗℘̃𝑖,1−(1−𝜐℘̃𝑖)𝑗).R=∑j=1nKj(μ℘˜ij,1−(1−υ℘˜i)j). (7) By applying the operations presented in Secti...