3. Show that if A is n xn and c is any real number, then det(CA) c" det (A) 4. Suppose that A is a square matrix, and n is some positive integer. Explain why it is true that An is invertible if and only if A is invertible..
4. (a) Find a 2 x 2 matrix A such that A 2, or explain why there is no such matrix b) Find a 3 x 3 matrix A such that A 13, or explain why there is no such matrix..
4. (6 pts) For the function f(x) =x^2 - 4x: a. Determine the average rate of change from x = 1to x =4 b. Determine the instantaneous rate of change at x = 1..
3.2. Diagnostics 3, use the attached Minitab output to answer following questions the For the example in part model using the o.os that don't b) Identify influential cases using the recommended method in the textbook. c) Is there any multicollinearity exists why or why not? the multicollinearity? d) If yes,.
4. (1 point) A projectile is fired northward out to the sea from the top of a seaside cliff 384 ft high. The projectiles initial velocity vector is v(0) = ?0, 200, 160?. In addition to a downward gravitational acceleration of 32 ft/s2, it experiences in flight an eastward acceleration.
Question
3. The surface S is the portion of the graph z=xy over the unit disk.
a). Write down the integral that represents this surface.
b). Estimate the value of this integral, (and please provide sketch of this surface if possible)
.
4. [Subspaces]
Recall that, a nonempty subset W of a vector space V is a subspace of V if and onlyif the following two conditions are satised for any vectors u, v in W and any scalars c
in R:
(I).
4. A correlation matrix can be used to
A. All of these answers are correct.
B. estimate the coefficient of determination.
C. identify the strength of the relationship of the independent variables with the dependent variable.
D. estimate.
3. Using Venn diagrams, test each of the argument forms below for validity. Be sure to indicate how the diagrams you draw support your verdict.
a)
All S are P.
No P are M.
Some S are not.
4) a) Find all solutions of sinhz = -i b) Evaluate and express your answer for the following expression in rectangular form 4 angle 50 + 10e^i 7/18 pi 3) a) cos z = -31. b) Find all solutions of sinhz = 0.
4. a) Form the truth tables for NAND (the logical negation of the AND operator) and NOR (the negation of the OR operator). b) By using a truth table, prove that ( P) ( Q) = (P VQ)..
35 marks 3. Cereal Tasting: A ood processing company is interested in comparing the taste of siz new brands (A, B, C, D, E and F of cereal. Subjects will be asked to taste cereals and score them on a scale of 0-100, where higher scores indicate better taste. a).
3. When one is driving on dry asphalt, the distance in feet, d, to stop a car going S miles per hour is modeled by the formula S=sqrt(22.5d) If Mark's car is going down a street made of asphalt and he is driving at 25mph and slams on the brakes,.
4. (20 points) For 4 choices A,B,C, and D, a decision-maker has the following pair-wise comparison matrix and rankings of the confidence in their validity: A B C D (1) B vs. D Highest A 1 2 1/3 3 (2) A vs. D B 1 4 1/2 (3) B vs..
3. Use matrix algebra to estimate the coefficients of the model y = b0 + b1x1 + b2x2 + e.
4. Interpret each of the coefficients in the model from question 3.
5. Calculate the variance-covariance matrix for the model estimated in question 3.
.
4) Find the inverse of f(x)=1+3x/5-x is not equal to 5/2
2)Find all the zeros of the polynomial and write the polynomial in factored form. ( 14 points)
Use Descartes rule of sign to determine how many positive and how many negative zeros the.
4) Find the inverse of functions
a) f: R -> R, f(x) = (5x + 3)/8;
b) f: R - {-5/2} -> R - {3/2}, f(x) = 3x/(2x + 5);
c) f: R+ -> (0,1), f(x) = 1/(x + 1);.
