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Solving Algebraic Equations

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.

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Solving Algebraic Equations

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  1. Math Review with Matlab: Solving AlgebraicEquations 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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)]

  7. Roots are Complex Conjugates 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]

  8. 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

  9. s is a structure 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]

  10. 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

  11. 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

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