Math Review with Matlab Solving Algebraic Equations with
Math Review with Matlab: Solving 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: Multiple Variables Solving Algebraic Equations with Multiple Variables n Solve Command for Equations of Multiple Variables n Single Equation of Two Variables Example n Two Variable Complex Solution Example n System of Equations with Symbolic Constant Example 2
Solving Algebraic Equations: Multiple Variables Solve Command for Equations of Multiple Variables n n n 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 3
Solving Algebraic Equations: Multiple Variables Single Equation of Two Variables Example n 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 4
Solving Algebraic Equations: Multiple Variables Default Solution n n 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 5
Solving Algebraic Equations: Multiple Variables Solve for b n n 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)] 6
Solving Algebraic Equations: Multiple Variables Two Variable Complex Solution Example n n 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 7
Solving Algebraic Equations: Multiple Variables System of Equations Example n Solve the system of consistent linear equations: » » » syms x 1 x 2 x 3 f 1='3*x 1 -x 2+2*x 3=12'; f 2='x 1+2*x 2+3*x 3=11'; f 3='2*x 1 -2*x 2+x 3=2'; [x 1 x 2 x 3]=solve(f 1, f 2, f 3) x 1 = 7 x 2 = 5 x 3 = -2 8
Solving Algebraic Equations: Multiple Variables System of Equations with Symbolic Constant Example n Solve the two equations: n n 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 is a structure s = x: [1 x 1 sym] y: [1 x 1 sym] 9
Solving Algebraic Equations: Multiple Variables Viewing Structures n n n The solution is a structure with named fields x and y representing symbolic expressions View each symbolic expression separately Expressions are in terms of symbolic variable a s = x: [1 x 1 sym] y: [1 x 1 sym] » xs=s. x xs = 18/5+1/5*a » ys=s. y ys = -3/5+2/15*a 10
Solving Algebraic Equations: Multiple Variables Summary n n 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 11
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