OC userin StatisticsΒ·1 May 20186. The system of equations x + y - 122 = 6 3x + y - 22 = 0 2x + y - 8z = 3 A) Has a unique solution, because the determinant of the coefficient matrix is zero. B) Has infinitely many solutions, because the determinant of the coefficient matrix is nonzero. C) Has a unique solution, because the determinant of the coefficient matrix is nonzero. D) Has infinitely many solutions, because the determinant of the coefficient matrix is zero. E) None of the above.
OC userin StatisticsΒ·30 Apr 2018(b) Determine values for constants a, b β if any β that will make lim (V x2 β 2 + 1 β ax β b) = 0. ANSWER ONLY
OC userin StatisticsΒ·23 Apr 2018(10) Find an equation of the tangent line to the curve r? - x*y+ 2y2 = 7 at the point (-1,2).
OC userin StatisticsΒ·22 Apr 201812. Let y = f(x) be defined by the equation y + 12x2 + xe4y = 13 near x = 1, y = 0. The value of f'(1) is (a) β9, (b) β7, (c) -5, (d) -10, (e) -13.
OC userin StatisticsΒ·21 Apr 20184. Consider the function f(x) = 4x2 β 22 - 1 (a) [2 marks State the definition of a function being continuous at <= a.
OC userin StatisticsΒ·20 Apr 201814. The points Q = (0,1,-1), R= (1, 1,-1) determine a line. The shortest distance from S = (1,1,1) to this line is: -15 B) te % - i
OC userin StatisticsΒ·22 Apr 2018(c) Consider a 6 x 5 matrix M such that MX=0 has only the trivial solution X = 0. Find the dimension of the row space of M.
OC userin StatisticsΒ·16 Apr 20185. (15 marks) Let f(x) = (In x)2. (a) Determine the domain of definition and the roots of f.
OC userin StatisticsΒ·14 Apr 20182. (10 marks) et y = xy. Determine the (a) Consider the curve C implicitly defined by the equation equation of the tangent line to Cat(1,1). (6) Compute the derivative of y = (sin x) sin x.
OC userin StatisticsΒ·13 Apr 20182 2 5. Let A =( ). Which one of the following is true? LEA 26 ) (I is the 2 x 2 identity matrix) A) = 3 is an eigenvalue of A and is a corresponding eigenvector 2 (B) A +31 is not diagonalizable C) = 4 is an eigenvalue of A and is a corresponding eigenvector D) A is diagonalizable E) None of the above.
OC userin StatisticsΒ·11 Apr 201811 β’ -2 D a la-1 8. Let A = 1 la-9- 94 The linear system AX = B has: (A) more than one solution if and only if |al 3. (B) a unique solution if and only if |al + -3. (C more than one solution if a = -3. ((D) ho solution if a = 3. (E)None of the above. (Exactly one of the above statements is true.)