You will NOT earn any credits unless you show the intermediate steps to obtain your solution and the final solution is exactly correct. (1) (16 points) Apply the Gauss-Jordan method to find the inverse of the following matrix A= ┌ ┐ │1 1 1│ │0 2 3│ │5 5 1│ └ ┘ (2) (7 points for each sub-problem) find dy/dx. (a) y = lnx ∫ e^(-t) dt, x>0 2 (b) y = 3x+2 ∫ (1+t^3) dt. 0 (3) (7 points for each sub-problem) Evaluate the integral. (a) ∫xcos(x^2-1)dx　　　　 　(b) ∫(x-1) / (1+4x-2x^2) dx (c) ∫[sex(x‧e^tanx)]^2 dx (d) ∫(√1+lnx)‧lnx/x dx (e) π/6 (f) 3 ∫ (sinx)^2‧cosx dx ∫ x^2‧e^(-x) dt -π/6 0 (g) π (h) π/4 ∫ (e^cost)‧sin(2t) dt ∫ 2x‧cosx dx 0 0 (i) ∫sin(lnx)dx (j) 2 ∫ ln(x^2‧e^x)dx 1 (4) (10 points) Find the eigenvalues and their corresponding eigenvectors of the matrix A= ┌ ┐ │ 1 1 │ │-2 4 │ └ ┘ --

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