Hi, I'd like some help with number 4.1 and 4.2 

programming on Cmap only.

Thank you

 

BCEE 231 Homework problems P4P.4.1BCEE 231 – HomeworkSet#4P4.1[30 marks]Given the following two matrices (as sample data)31 12 0102412221 32 12−==−−−ABwe can form the matrixC=A– βBwhere βis a scalar value.Except for a few special values of β, the solution vectorXofC X= 0 is the trivial nullvector. In many engineering problems1, we want to find these special values of β thatmakes the solution vectorXnon-trivial.There are three such special values of β (the so-called the eigenvalues) for the givensample matrices. They are found as the values that make the determinant ofCzero asshown in following program segment:main(){defmat(A[N = 3,N], 3, 1, -1, 0, 2, 4, -2, 1, 3);defmat(B[N,N], 2, 0, 1, -1, 2, 2, 2, -1, 2);// Find b that makes the determinant of (C = A-b*B) equal 0// Explore range of roots b'sclearplot(); plot(x, -0.5, 5, Det(x));zero(Bet[N]);// Storage for the roots (eigenvalues b's)tol# = 1.e-8; // Reduce tolerance for more accurate rootBet[1] = root1(b, -0.5, 0.5, Det(b));Bet[2] = root1(b, 0.5, 2, Det(b));Bet[3] = root1(b, 2, 5, Det(b));print(Bet,^^,"Residuals=",Det(Bet[1]),Det(Bet[2]),Det(Bet[3]));}Det(float b){ // Return the determinant of C = A-b*Breturn det(!C = A-b*B);}1Such as the problems of natural vibration and stability of structures.

Attachments:

• 1494298832-BCEE231- Homework Problems Set 4.pdf