Q.37: Find the Eigen values and Eigen vectors for the matrix A: RGPV DEC 19 Q.38: Show that the following equations are consistent or not. 5x + 3y +14z = 4, y + 2z = 1, x-y+2z = 0 RGPV DEC 19 Q.39: Evaluate by expressing the following limit of a sum in the form of a definite integral. - Q.40: Verify Lagrange's mean value theorem for the function f(x) = 2x2-7x+10 in the interval [2, 5]. Q.41: If u = f(y-z, z-x, x-y ) prove that du/dx + du/dy + du/dz = 0 Q.42: Evaluate ∫ 0,2 ∫ 0,1 ( x^2 + y^2) dx dy Q.43: Evaluate ∫0,a∫0,x∫0,x+y e^(x+y+z) dz dy dx Q.44: Find rank if the matrix [1 2 3 2, 2 3 5 1, 1 3 4 5] Q.45: Solve the system of equations 3x + 3y + 2z =1; x + 2y = 4; 10y + 3z = –2 and 2x – 3y – z = 5