39730

-10x₁  + 10x₃ + 2x₄ – 9x₅                     = 79.79

-4x₁ + 8x₂ + 3x₃ – 5x₄ + 3x₅                 = 117.87

10x₁ – 9x₂ + 4x₃ + 9x₄ – x₅                   = -76.99

4x₁ + 2x₂-7x₃ – 8x₄ + 2x₅+ x₅²             = -71.82

-3x₁– 9x₂ + 5x₃ – 3x₄ + 4x₅                         = -28.94

3x₁ + 10x₂-5x₃+6x₄ + 5x₅                    = 97.65

1, calculate rank of matrix A

2, calculate rank of Augmented Matrix

3, if there is a unique solution, calculate it

Yes the equation has unique solution. Value of variables is

x1=-4.5081

x2=9.9993

x3=7.5017

x4=3.7065

x5=5.2901

x6=-2.2025

4, Explain how you deal with quadratic functions in system of equations

For quadratic equation we first define the variable x as a system parameter. Now using coefficients we find discriminant of the equation and based on sign of discreminant we solve the equation.

5, explain how quadratic functions are entered in MATLAB when analysing matrixes

In matlab function quadratic(a,b,c). The function quadratic requires three input arguments A, B, and C (the coefficients of the quadratic equation ax2 + bx + c = 0), but provides no output.

First, calculate the value of the discriminant.

If the disciminant is positive, there are two real solutions, given by the quadratic formula . If the discriminant is zero, then the quadratic formula provides a single solution, namely x = −b/(2a). If the discriminant is negative, then there are no real solutions (we cannot take the square root of a negative number). This calls for an if..elseif..else conditional.