ME102 EXAM II (Sample Exam)Questions 1 through 4 deal with the following set of linear equations:to be expressed in standard form:[A]{X} = {B}where standard 1-based index numbering is used (not the 0-based default used by MathCAD).(1) What is a12?(a) −3(b) −2(c) −1(d) 2(e) 3(2) What is a23?(a) −3(b) −1(c) 0(d) 2(e) 3(3) What is b3?(a) −3(b) −2(c) 0(d) 1(e) 3(4) What is the size of [B]?(a) 1 x 3(b) 0 x 3(c) 3 x 0(d) 3 x 1(e) 3 x 3x12x3⋅− 3x2⋅x23+ x3x3x1− 2+ x2− 0Questions 5 through 11 deal with the following MathCAD code for a set of linear equations instandard form [A]{X} = {B}Assume all evaluations in the questions below occur below the MathCAD code shown above.(5) A1,1 =(a) 1(b) 2(c) 3(d) 4(e) 5(6) X1 = (a) -1(b) 0(c) 1(d) 2(e) 3(7) What is the size of W?(a) 1 x 1(b) 1 x 2(c) 2 x 1(d) 2 x 2(e) 4 x 4(8) Y0,1 = (a) 0(b) 1(c) 2(d) 4(e) 10(9) Z1,1 = (a) -1(b) 0(c) 1(d) 2(e) 4A1324:= B1−1−:= Xx1x2XA1−B⋅:= YAA⋅:= ZAA1−⋅:= VAT:= WVB⋅:=(10) V1,0 =(a) 1(b) 2(c) 3(d) 4(e) 5(11) If using Cramer’s rule to find the second unknown variable x2 with |A2|/|A|, what wouldyou use for |A2|?(a) -2(b) 0(c) 2(d) 6(e) 10(12) A linear system [A]{X} = {B} is said to be ill conditioned if |A| is(a) a very large positive number(b) a very large negative number(c) 1(d) -1(e) very small (close to 0)(13) After the MathCAD code below, to what value would z evaluate?(a) 1(b) 2(c) 3(d) 4(e) 6j1− 1, 5..:= zj1∑:=Questions 14 through 17 deal with using the Newton-Raphson method to solve the following setof nonlinear equationsusing the MathCAD iterative formula:(14) What is the size of Z?(a) 1 x 3(b) 3 x 1(c) 0 x 3(d) 3 x 0(e) 3 x 3(15) What is the correct expression for the first (0th) element of the Fi vector?(a) 1(b) x(c) x − y + z(d) x − y + z + 5(e) x − y + z − 5(16) Using MathCAD 0-based array subscripts, what is the correct expression for Z0,1?(a) 2(b) 0(c)−1(d)−2(e) 2(x − 1)(17) Using MathCAD 0-based array subscripts, what is the correct expression for Z2,1?(a) 1(b) 0(c)−1(d)−1 − z(e) z − 1xy− z+ 52y x 1−()2Xxyzx1x2x3X0X1X2zy⋅ xy−Xi1+XiZ1−Fi⋅−Questions 18 through 19 deal with the following MathCAD code:Assume all evaluations in the questions below occur below the MathCAD code shown above.(18) X0 = (a) 1(b) 2(c) 3(d) 4(e) 5(19) Y2 = (a) 1(b) 2(c) 3(d) 4(e) 5(20) A local maximum of a function f occurs where(a) f’ = 0 and f’’ < 0(b) f’ = 0 and f’’ > 0(c) f’ < 0 and f’’ = 0(d) f’ > 0 and f’’ = 0(e) f’ = 0 and f’’ = 0A147258369:= XA1〈〉:= YAT()0〈〉:=Questions 21 through 24 deal with performing a Golden Section search maximization with aninitial interval of where the two interior points for the first iteration would be 0.62 and0.38. The values for the function f(x) at the first iteration points are:f(0) = 1, f(.38) = 3, f(.62) = 2 f(1) = 1(21) What is the best estimate for the optimal x in the first iteration?(a) 0(b) .38(c) .62(d) 1(22) What would be used for the lower end of the x interval in the second iteration?(a) 0(b) .38(c) .62(d) 1(23) What would be used for the upper end of the x interval in the second iteration?(a) 0(b) .38(c) .62(d) 1(24) What would be the approximate value for interior point x2 in the second iteration?(a) .24(b) .38(c) .62(d) .86(e) 1(25) What is the next number in the Fibonacci series: 0, 1, 1, 2?(a) 2(b) 3(c) 4(d) 5(e) 6(26) What is the x component of the gradient of the function f(x,y) = xy2 − x2y at the point (1,2)?(a) -3(b) 0(c) 1(d) 2(e) 40x1≤≤(27) What is the y component of the gradient of the function f(x,y) = xy2 − x2y at the point (1,2)?(a) -3(b) -1(c) 0(d) 1(e) 3(28) What is the length of the gradient vector of the function f(x,y) = 3x + 4y at the point (-1,1)?(a) 1(b) 3(c) 4(d) 5(e) 7(29) If using the steepest ascent method to maximize a function with a gradient vector i + 2j atthe point (2,1), where the optimal step size h is found to be 2, what would be used for thex coordinate in the next iteration?(a) 1(b) 2(c) 3(d) 4(e) 5(30) For the vectorswhat would the MathCAD function slope(x,y) return?(a) -1(b) 0(c) 1(d) 2(e) 3(31) For the vectorswhat would the MathCAD function intercept(x,y) return?(a) -1(b) 0(c) 1(d) 2(e) 3x123:= y222:=x123:= y222:=Question 32 through 34 deal with using natural logarithms to perform a linear regression of theexponential equation y = aebx. The linear regression equation will be of the form:Y = a0 + a1X(32) What should be used for Y?(a) ln(y)(b) 1 / ln(y)(c) ey(d) 1 / ey(e) y(33) What should be used for X?(a) ln(x)(b) 1 / ln(x)(c) ex(d) 1 / ex(e) x(34) If a0 and a1 are found, what is the correct expression for b?(a) exp (a0)(b) exp (a1)(c) a0(d)