Which of the following is FALSE? A. Det (AB) = Det (A) + Det (B) B. Det (AB) = Det (A) Det (B) T C. Det (A¹) = Det (A) D. The determinant of a matrix can be a negative number.

Q: Write the equations in cylindrical coordinates. (a) 5x² - 7x + 5y² + z² = 7 (b) z = 2x² - 2y²

A:

Q: a) y" - 2y³ +y = 4 cos x y" - y = cos (2x)

A:

Q: Suppose a pendulum of length I meters makes an angle of radians with the vertical, as in the figure.…

A:

Q: Which of the following is NOT always true for sets A and B such that AC B? A. AnB = A C. BU (A - B)…

A:

Q: Determine if the graph can represent a polynomial function. If so, assume that the end behavior and…

A: The graph of a polynomial function is a continuous curve which has no breaks. From the graph of a…

Q: lower corner of a leaf in a book is folded over so as the inner edge of the page. Show that the…

A:

Q: Donald owes the bank $9450. To repay his debt, he paid a fixed amount back to the bank each month.…

A:

Q: Four coins are tossed, and the number of heads is recorded. Shade the region on the histogram that…

A:

Q: 17. Show that if A and B are sets in a universe U then ACB if and only if AUB=U.

A:

Q: 3. Let be the Euler phi function. (d) If mn, show that o(m) (n). (e) Let (n) denote the sum of the…

A:

Q: Find the sum of the infinite geometric series 4 8 + 9 27 2 3 - - 16 81 +.

A: A sequence is a set of numbers that has a particular order or obeys a general form. The series is…

Q: 1. Let's take a look at limits of functions at infinity. Given a function f: R→ R and some LER, we…

A:

Q: 2- Manually calculate the following. a. 9100 (mod 11) b. 13241 (mod 35)

A:

Q: Suppose you are invited to play a game in which you bet $1 on any number from 000 to 299. If your…

A:

Q: Find the volume of the solid bounded below by the circular paraboloid z = : x² + y² and above by the…

A: Solution:

Q: ∞ For r < 1, n(n-1)² = 2² +6³ +12r²¹ +….. the power series for f(x) = 21² (1+z)³ 27² (1-r)³ 1 Use…

A: Given that for r&lt;1,∑n=0∞n(n-1)rn=2r2+6r3+12r4+ . . . =2r2(1-r)3. By using this to find the power…

Q: H 28. For all integers a, b, and c, if a b and a/c, then al(b + c).

A:

Q: Q.#15 Please prove the following trig identities/equalities. To do so, start with LHS (or RHS) and…

A:

Q: Find the values of x so that the series below converges. 8 n=1 xn 11"

A:

Q: Use synthetic division to divide 2x5 + 5x4 ─ 2x3 + 2x2 ─ 2x + 3 by x + 3.

A: Synthetic division is a method used to perform the division operation on polynomials when the…

Q: (1) Give an example of perfect groups (i.e. the group equals to its own com- mutator subgroup). (2)…

A:

Q: A rhombus ABCD is such that: 1. A = (-1, 3, -1) 2. B lies on the line I with vector equation: [-1 0…

A:

Q: 1 E x² + y² + z² 2 = 25 and x² + y² + z² Evaluate J x² + y² + z² dV, where E lies between the…

A: Given that the spheres,          x2+y2+z2=25, and x2+y2+z2=49, in the first octant.

Q: 2. Determine whether the set S = {(2,1,0), (-1,0,1), (8,3,-2) } is linearly independent or linearly…

A:

Q: The given contingency table lists the cross tabulation of whether adults, for whom answering the…

A:

Q: angle, more general (example: 0-104 Solve 2 cos 0+1=0 for the following angles. a) [0, 2π) b) any…

A:

Q: Answer the following questions. Assume A is a 3 x 3 matrix. Then • If the column space C(A) is a…

A: Given A is a matrix of order 3  Dimension of column space is rank  Dimension of null space is rank…

Q: Finally, let f(x) = S. Then, by the division algorithm in k[x], there exist polynomials q(x) and…

A: This is the division algorithm for polynomials. The doubt has been explained in step 2. Go through…

Q: Find Fourier series of ?(x) = { TT, -IT, -1<x<0 0<x< 1

A:

Q: Suppose that f(z) is entire and that the harmonic function u(x, y) = Re[f(z)] has an upper bound uo;…

A: It is given that fz is entire and ux,y=Refz and is bounded above by u0. The objective is to use…

Q: w using Exponential Shift; m = 2 & n =4 y" + 2y' + y = menx

A:

Q: e each percent as a decimal and as a mixed number or fraction i lest form. (Examples 1-3) 50% =…

A:

Q: (a) Find the following determinants. 1 2 -1 -2 787 296 3 -3 1.67291

A:

Q: What can you say about the sets A and B if AB=A?

A: Consider two sets A  and B. Then the symmetric difference between these two sets is denoted by A⊕B.…

Q: 1) The diagram shows the graph of y = x² - 2x - 8. The graph crosses the x-axis at the point A and…

A: The given problem is to factorise the given equation and also find the co-ordinates of A and B shown…

Q: Calculate the missing information. Round dollars to the nearest cent and percents to the nearest…

A:

Q: a) Consider the following game matrix: Use the Simplex method to find optimal solutions to each…

A:

Q: If my goal is to determine whether vectors dent or independent, I will solve the system (Do not…

A:

Q: 2. let where a) why why be ([^]) = [24] 2x L: IR→ L did we use just ь) із sketch Sketch the the…

A: This is a question of Linear transformation.

Q: A rectangle is inscribed in the region bounded by the graph of y= e1-2x^2  and have one of its side…

A: The area(A) of a rectangle is calculated using the formula: A=lw, where l, w are the length, width,…

Q: Elimination Tournaments In an elimination tournament the teams are arranged in opponent pairs for…

A:

Q: You roll a 6-sided die. What is the probability that you will roll either a 4 or a 3? P(4 or 3) =…

A:

Q: (a) Any subspace must contain a zero vector. T F

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: 3. For each of the following spaces, say if they are or if they are not sequentially compact,…

A: 3. The given induced Toplogies are  (a) A=z:z&lt;1  or  z&gt;2⊂ℂ with the induced topology as a…

Q: 1 SS √ ₂ 20² + y² + 2² Evaluate x² + y² + ₂²: dV, where E lies between the spheres x² + y² + z² = 1…

A:

Q: Fill up the membership table to prove the set identity AnB = AUB. Note that 1 means "is an element…

A:

Q: Q#12 Please prove that cos(a− ß) cos(a+ß) = (cosa cos 6)²-(sina sin 6)²

A:

Q: 4.50. Verify Green's theorem in the plane for fx²ydx + (y² - xy) dy where C is the boundary of the…

A:

Q: Given vectors in R2, A = -4i + 3j, B = 3i-2j, C = -3i+ j. What is (A C) B ?

A:

Q: n Rn ² = ²/12 (-8 + + ²). n lim Rn n→→∞ = dx.

A: