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lavster
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when solving a system of simultaneous equations in matrix from (with the LHS = 0) why does the determinant of the matrix need to vanish?
thanks
thanks
lavster said:when solving a system of simultaneous equations in matrix from (with the LHS = 0) why does the determinant of the matrix need to vanish?
thanks
Simultaneous equations are a set of equations that contain two or more unknown variables and must be solved simultaneously for all the variables.
Solving simultaneous equations allows us to find the values of the unknown variables that satisfy all the equations in the set. This is useful in various fields of science, such as physics, engineering, and economics, where multiple variables are involved in a system.
There are several methods for solving simultaneous equations, including substitution, elimination, and graphing. The most commonly used method is substitution, where one equation is solved for one variable and then substituted into the other equation to find the value of the remaining variable.
Yes, simultaneous equations can have any number of unknown variables. However, the number of equations in the set must be equal to the number of unknown variables in order to find a unique solution.
If the number of equations in the set is equal to the number of unknown variables and the equations are independent (not multiples of each other), then the set of equations will have a unique solution. If the number of equations is less than the number of unknown variables, there will be infinitely many solutions, and if the equations are inconsistent, there will be no solution.