Solving Algebraic Equations 4/11/2017 Math Review with Matlab: Solving Algebraic Equations Algebraic Equations with Multiple Variables S. Awad, Ph.D. M. Corless, M.S.E.E. D. Cinpinski E.C.E. Department University of Michigan-Dearborn

Solving Algebraic Equations with Multiple Variables Solve Command for Equations of Multiple Variables Single Equation of Two Variables Example Two Variable Complex Solution Example System of Equations Example System of Equations with Symbolic Constant Example

Solve Command for Equations of Multiple Variables The solve command can be used to solve symbolic expressions with more than one variable: solve(f) solves the symbolic expression f using the symbolic variable closest to x as the independent variable solve(f, v) solves the symbolic expression f in terms of the independent variable v

Single Equation of Two Variables Example Given the equation: 1) Find the solution of the equation assuming that c is the solution variable 2) Find the solution of the equation assuming that b is the solution variable

Default Solution Solve for c as the independent variable c is the default variable since it is closest to x » syms b c » f=b^2+4*c+2*b; » sol_c=solve(f) sol_c = -1/4*b^2-1/2*b

Solve for b Solve for b as the independent variable b must be explicitly specified on the command line » sol_b=solve(f,b) sol_b = [ -1+(1-4*c)^(1/2)] [ -1-(1-4*c)^(1/2)]

Two Variable Complex Solution Example Given the equation of two variables: Solve for x in terms of y using Matlab: » syms x y » xs=solve(x^2+9*y^4) xs = [ 3*i*y^2] [ -3*i*y^2] Roots are Complex Conjugates

System of Equations Example Solve the system of consistent linear equations: » syms x1 x2 x3 » f1='3*x1-x2+2*x3=12'; » f2='x1+2*x2+3*x3=11'; » f3='2*x1-2*x2+x3=2'; » [x1 x2 x3]=solve(f1,f2,f3) x1 = 7 x2 = 5 x3 = -2

System of Equations with Symbolic Constant Example Solve the two equations: x and y are independent variables a is a constant » syms x y a » s=solve(x+6*y-a,2*x-3*y-9) s = x: [1x1 sym] y: [1x1 sym] s is a structure

Viewing Structures The solution is a structure with named fields x and y representing symbolic expressions s = x: [1x1 sym] y: [1x1 sym] » xs=s.x xs = 18/5+1/5*a » ys=s.y ys = -3/5+2/15*a View each symbolic expression separately Expressions are in terms of symbolic variable a

Summary The solve command can be used to solve: A single equation in terms of an independent variable A system of multiple consistent equations A system of equations having symbolic variables and symbolic constants