types of solution of system of linear equation

'Standard Form' is #ax+by=c# where #a#, #b# and #c# are constants (numbers). We'll look at two ways:Ī linear equation can be written in several forms. (a) A system of $5$ equations in $3$ unknowns and it has $x_1=0, x_2=-3, x_3=1$ as a solution.We'll make a linear system (a system of linear equations) whose only solution in #(4, -3)#.įirst note that there are several (or many) ways to do this.

The Possibilities For the Number of Solutions of Systems of Linear Equations that Have More Equations than Unknownsĭetermine all possibilities for the number of solutions of each of the system of linear equations described below.

Thus there are infinitely many solutions. The rank is $r=2$ and the number of variables is $n=3$. Hence the system is inconsistent.Ī homogeneous system is consistent. However, the second row means that we have $0=1$. The last matrix is in echelon form and it has two nonzero rows. The possibilities for the solution set of a system of linear equationsĪn $m imes n$ system of linear equations isĪ_ (j) A homogeneous system of $4$ equations in $3$ unknowns and the rank of the system is $2$.(i) A system of $3$ equations in $2$ unknowns and the rank of the system is $2$.(h) A homogeneous system of $5$ equations in $3$ unknowns and the rank of the system is $3$.(g) A homogeneous system that has $x_1=3, x_2=-2, x_3=1$ as a solution.(f) A homogeneous system of $3$ equations in $4$ unknowns.(e) A homogeneous system of $4$ equations in $4$ unknowns.(d) A system of $2$ equations in $3$ unknowns that has $x_1=1, x_2=-5, x_3=0$ as a solution.(c) A system of $5$ equations in $4$ unknowns.(b) A homogeneous system of $5$ equations in $4$ unknowns.(a) A homogeneous system of $3$ equations in $5$ unknowns.the possibilities for the solution set of a system of linear equations.(j) A homogeneous system of $4$ equations in $3$ unknowns and the rank of the system is $2$.

(h) A homogeneous system of $5$ equations in $3$ unknowns and the rank of the system is $3$. (g) A homogeneous system that has $x_1=3, x_2=-2, x_3=1$ as a solution. (f) A homogeneous system of $3$ equations in $4$ unknowns. (e) A homogeneous system of $4$ equations in $4$ unknowns. (d) A system of $2$ equations in $3$ unknowns that has $x_1=1, x_2=-5, x_3=0$ as a solution. (c) A system of $5$ equations in $4$ unknowns. (b) A homogeneous system of $5$ equations in $4$ unknowns. (a) A homogeneous system of $3$ equations in $5$ unknowns.

In this post, we summarize theorems about the possibilities for the solution set of a system of linear equations and solve the following problems.ĭetermine all possibilities for the solution set of the system of linear equations described below.

Types of solution of system of linear equation