Let A and B be square matrices of the same size. Prove that if A and B are both upper triangular, then AB is upper triangular. If A and B are both upper triangular, do they necessarily commute? If you think they must commute, give a proof; if you think they might not commute, give a counterexample.

Q: With the aid of Wronskian: f(x)=sin(2x); g(x)=cos(x)sin(x)

A: Given,             To evaluate the Wronskian.

Q: A crossed belt connects a 16-centimeter pulley (x = 8-cm radius) on an electric motor with a…

A: Given information:The radius of pulley on saw and motor is 16 cm and 8 cm respectively, which…

Q: Determine equation of the polynomial function in factored form and IN THREE POSSIBLE WAYS if “A…

A: Given Information:The quartic function with real zeroes only at  and a point  on its graph.To…

Q: Find a side and diagonal relationship to find √10. Then use it to find an approximation to √10…

A: To find a side and diagonal relationship to calculate √10, consider a right-angled triangle where…

Q: A car rental agency in a major city has a total of 4600 cars that it rents from three locations:…

A: A car rental agency in a major city has a total of 4600 cars that it rents from three locations:…

Q: Show that in any field F, the equation ² = two solutions. Can you think of a field in which the…

A:

Q: Write an equation that "works" for the polynomial shown at the right (factored form is fine). Please…

A: We have to find the equation of the given graph

Q: Complete the following related rates word problem. Include a well-labeled figure and supporting…

A: A 10-foot-long trough has right trapezoidal ends perpendicular to the length. Each trape- zoidal end…

Q: Determine if v is an eigenvector of the matrix A.

A: To determine whether v is an eigenvector of the matrix A.Thus it must satisfy that

Q: 3. Determine whether the vectors u=(1,2.1), v=(2,1,1), w=(7,4,1) of R^3 are linearly independent or…

A: Let  u=(1,2,1) v=(2,1,1) ,w=(7,4,1)Let , au+bv+cw=0i.e,

Q: Evaluate (2+ it)² dt and f sin(2it) dt.

A:

Q: 1. Determine the radius of convergence of the series Σar", where an is given by: (a) 1/n". (b)…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Find the inverse laplace of e⁻²ˢ/s³

A:

Q: (1) Statics. What if there were three unknown weights and three different scales balanced with those…

A:

Q: Approximate the following integral using Gauss quadrature 1.5 =/e-x² Use 16 significant digits in…

A:

Q: 160 Find the center of mass of the lamina bounded above by f(x) = x² + 4x + 2 and below by g(x)=x+2…

A: Let us solve above problem using related formulea.

Q: Illustration (a) below shows a portion of the game board before and illustration (b) shows it after…

A: Illustration (a) below shows a portion of the game board before and illustration (b) shows it after…

Q: (a) Write down the equation of motion for the point particle of mass m moving in the Kepler…

A: Since you have posted a question with multiple subparts, we will solve only the first three subparts…

Q: 1. A company sales representative estimates that her car's gas mileage averages 28 miles per gallon…

A: A company sales representative estimates that her car's gas mileage averages  miles per gallon on…

Q: 5. A recent college graduate has job offers for a sales position at two computer companies. Job A…

A: Job A pays: $50,000 per year plus 10% commission.Job B pays: $40,000 per year plus 20%…

Q: (e) If we have two sets A, BCR, A and B are both naturally increasing, then AUB is also naturally…

A: is natuarally increasing  if  s.t  and

Q: A sample of 20 plants was collected and the mean height was calculated as 8.3 cm. A 95% confidence…

A: Given ,Sample size n = 20mean height is 8.3 cm95% confidence level for the true mean(3.5 cm, 13.1…

Q: Consider the following graph of a system of linear inequalities: -10 -201 -10- O --1-0- 10 Knowing…

A: In this question, we will check the given points is the solution of the system.

Q: Supppose A is an invertible n x n matrix and v is an eigenvector of A with associated eigenvalue -4.…

A: A is an invertible  matrix and v is an eigenvector of A with associated eigenvalue .Using following…

Q: Prove the following statements. B. Let x EZ. If x² - 6x + 5 is even, then x is odd. C. Let x E R. If…

A:

Q: Consider the below 3 equations, U₁ = C1-C2 + C3 U₁C₁ + (0*C₂)+ (0*C3) = C₁ = U₁ = C1 + C2 + C3 In…

A:

Q: 5. (a) Give a proof by contradiction of: for all z e R, if a² is irrational, then z is irrational.…

A: Answer 5 (a)

Q: An object attached to a spring undergoes simple harmonic motion modeled by the differential equation…

A: Solution

Q: For each logical argument, select all the truth assignments for the propositional variables that…

A:

Q: A set of exam scores are approximately normally distributed with mean = 68 and standard deviation =…

A: Mean = 68 Standard deviation = 6

Q: Show that the following set is convex: with A € ST C₁ = {x R¹|x Ax ≤ 1},

A:

Q: Suppose that JCC is planning to offer courses in Finite Math, Applied Calculus, and Computer…

A: Given that:Each section of Finite Math can hold  students and bring in  in revenue.Each section of…

Q: (b) Given an ellipse with major axis = 16 units and minor axis = 12 units. Determine first 6 raster…

A: Given information:The major axis of the ellipse =16units.The minor axis of the ellipse…

Q: Draw examples of museums with only right-angled corners having 12 sides, 16 sides, and 20 sides that…

A: Given information: A museum with right-angled corners, and we need to determine the minimum number…

Q: 1) Mars Inc. claims that the produce M&Ms with the following distributions: 20% Yellow Red 30% 10%…

A: A bag of M&Ms was randomly selected from the grocery store shelf and the color counts…

Q: Perform one step of row reduction, in order to calculate the values for x and y by back…

A:

Q: (6) Let (G, *) be a group and a € G. Prove that the order of a is equal to the order of a-1. Prove…

A:

Q: Consider A= = If the G m Sc -2 -1 4 -1 - -1 1

A: We have to find q3 and columns of R

Q: . For n = 0, 1, 2, 3,..., let an = (a) Find lim sup(an)¹/", lim inf(an)¹/", lim sup|ªn+¹| and lim…

A:

Q: TET

A: We have to find the possible equation of the graph

Q: -) Consider the following graphical solution and Simplex Method path for an LP with objective…

A: From given feasible region we can write the associated mathematical form of LPP:sub to:…

Q: (6) xy + (1+x)y = r²e sin 3x with y(0) = 1

A:

Q: 1000m Find the length of the line AB in the figure below 47 58 5 49 A B

A: Given information:A quadrilateral along with the side length CD=1000m and the angles…

Q: a) Use the Euler formula, e¹⁰ (cos(0) + i sin(0))" = cos(n) + i sin(n). b) Suppose y(t) = e-2t eit…

A: In this question, we will find the solution to the given problem.

Q: 725 Differentiate function y using logarithmic differentation. (2-92)√√2+1 Hint: use logarithm on…

A:

Q: Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated…

A: Consider the given equation. and we have to find the value..Now, find the iteration.The number of…

Q: Make a sketch of a function, f(x), with the following properties: o domain {x|x > −8, x ≤ R} range{y…

A:

Q: Consider the function f(x) = (x − 2)^4 + (x − 2)^5. Minimize the function using the iterative method…

A:

Q: h Determine the value of h such that the matrix is the augmented matrix of a consistent linear…

A:

Q: The limit Lt (x,y) → (0,0) consider the 4Lt (x, me) → (0,0) Fonsider the Limit = 4+ has been defined…

A: The given limits,(a) (b) .The aim is to translate the given limit into digital format.