101 2 Given A = 14- (₁2 i ²₁ ) and B - ( ²1 2₂ ) = 1 1 a) b) Enter AT Enter BT B.

Q: Find an LU and LDU' factorization of the matrix A. A 435 89 5 8 -3 24

A: Given: A=4358958-324 To find: LU factorization of A LDU' factorization of A

Q: 19. Let X be any nonempty set, and let B = {{x}: x € X}. Show that B is a base for a topology on X.…

A:

Q: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x + x + x²…

A:

Q: Exercise 8.5.5. Use the following steps to prove that det(AT) = det(A): (1) First write PA = LU as I…

A:

Q: Let A and B be an n x n matrices. (a) (b) (c) BA. State the definition of an eigenvector of an n x n…

A:

Q: Evaluate the surface integral. y² ds, S is the part of the sphere x² + y² + 2² = 1 that lies above…

A: To Evaluate the surface integral. ∬Sy2 dS, S is the part of the sphere x2+y2+z2=1 that lies above…

Q: Calculate the following triple integral: 1 I = // / ₁ √² + R² + 2² where the solid S is defined as…

A: The solid S is given by S=x,y,z∈ℝ3:z2≤x2+y2≤2z-z2. This is the volume of the region that lies below…

Q: 1. Differential matters of (scalar) functions Let the (scalar) function f (x,y) in 2 variables, x, y…

A:

Q: A box with a lid has a length two times its width and a volume of 1000 cubic cm. If the minimum…

A:

Q: Find a basis of the kernel of the matrix [1 2 [1² 0 3 5 0 0 14 6 5] with a a 1 0 b= C = d = e || 0 C…

A: The given matrix is, 1203500146 and the basis a1000,b0c10,d0e01. To find the basis of a kernel of…

Q: Let T: P₂ → P₂ be a mapping defined by T(a + a₁x + a₂x²) = a₁ + a₁(x + 1) + a₂(x + 1)². (a)…

A: (a) Let, p1(x) = a0 + a1x + a2x2  ∈ P2               p2(x) = b0 + b1x + b2x2  ∈ P2     Let, α, β be…

Q: If T(x, y, z) gives the temperature in °C at a point (x, y, z), measured in feet from the center of…

A: Given that, Tx,y,z gives the temperature in degree C at a point x,y,z measured in feet from the…

Q: Find a set of vectors {u, } in R4 that spans the solution set of the equations {2w- w-x+z = 0, 2w +…

A:

Q: . f(t)=cosh6t d. f(t)=sinh8t   Solution step by step for Laplace USE INTEGRATION NOT DIRECT…

A:

Q: Q3 Fit a second-order polynomial to the data in the following table. 0.5 1.6487 Xi Y₁ 0 1 0.25…

A:

Q: Using: +∞ +∞ ** f(t)g(t)dt = 24/7 ** F (as) g(c)da 1217 F(w)g(w)dw 2π ∞ ∞ and a pair of known…

A:

Q: 21. f(x, y) = x² - y²; P(-1, -3); 3 4 5 5 "

A: The directional derivative of f(x,y) in the direction of a unit vector u⇀ at a point P0 is…

Q: 5) For the function f(x, y) = x ln(x y²) and g(x, y) = √√x² + y2, answer the following: a. For f(x,…

A:

Q: Determine whether the following series converge. Rigorously justify your answers (using the…

A:

Q: Question 2 Solve the following equation - list solutions separated with a comma, no spaces: y²-10y +…

A: The given equation is           y2 - 10y + 25 = 0       => y2 - 2.y.5 + 52 = 0        => (y -…

Q: Polynomial Equations MHF4U 3) Explain how you would use the Rational Zero Theorem to determine…

A:

Q: Co1.1 Identify applicable methods, techniques, and fundamental principles of numerical methods to…

A: Where the functions meet or intersect at points these points are called roots of the given functions…

Q: fff z dx dy dz 22²² + y ², V: Z = Z=4

A:

Q: 9) g(x)=x² + 8x - 18 Vertex: Axis of Symmetry: Vertex Form of g(x):

A: Since you have posted a multiple question according to guildlines I will solve first(9)   question…

Q: A region in the xy-plane is bounded by the curves y = cos x and y = π2/4−x2 for −π/2 ≤ x ≤ π/2.…

A: We draw the graph of given function.. So clearly intersect at point ±π/2

Q: Consider the function: f (x,y) = 2x² - 4x - xy² + 2y² - 3. Show and explain that the stationary…

A: The answer provided below has been developed in a clear step by step manner.

Q: 4) Using the Laplace Theorem for Division by Power of t, evaluate (sinh 3t) t

A:

Q: ing to λ. Find h in the matrix A below such that the eigenspace for λ=5 is two-dimensional. -263 3h0…

A:

Q: The vector x is in a subspace H with a basis B = {b₁,b₂). Find the B-coordinate vector of x. 1 - 3…

A:

Q: 5. Find the domain of the function. (a) f(x)=4-5x+x² (b) f(x)= 1 x² - 6x+5

A:

Q: factorise the following: a. 4y +4 (2y) + 4 b. 108q -36 +7q3 -59q2

A: We will use middle term factorization and vanishing method to factorize.

Q: Calculate the finance charge (in $) and the annual percentage rate for the installment loan by using…

A:

Q: Sheila draws an angle measured in radians on a unit circle in the coordinate plane. She claims there…

A: To find the value of k for which sin(a + kπ)=sin(a) .

Q: Find the inverse of the matrix A, if it exists. A 02 -407 0 2 0

A: I have explained everything with in the solution. Please go through that.

Q: Consider the matrix (a) (b) Find the eigenvalues of A. A = [2 0 1] 0 1 0 102 Find a basis for the…

A:

Q: Emily wants to buy a car, there is a dealership giving her 0% financing for 24 months. The price of…

A: Sol:- i) Let the balance in the savings account at time t be denoted by B(t). Then, the rate of…

Q: Find the characteristic polynomial and the eigenvalues of the matrix. -7 -3 M 1 -1 The…

A: Given that the matrix A=-7-31-1     .

Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw() = 4 6 V= 19 16 and -5

A:

Q: 1. Consider the following payoff matrix: b) Player 1 Strategy B Strategy A Player 2 Strategy A…

A: The payoff matrix for a two player game with two strategies is given as follows     player 2…

Q: Jeremy and Thulile are running toward the point P along two straight paths that make a fixed angle…

A: Given: Jeremy and Thulile are running toward point P along two straight paths that make a fixed…

Q: blem #5: Consider the matrices A = 2 0 7 6 -2 8 0 0 0 28 21 24 3 -4 -14 24 b = 18 18 3 Which of the…

A:

Q: M₁ 1 Use the Gram-Schmidt procedure to produce an orthogonal set with the same span Hint it you have…

A:

Q: Prove that any isosceles trapezoid is cyclic. You should use the inclusive definition of…

A: Here we want to prove that isosceles trapezoid is cyclic.

Q: 2. Find a basis for the set of vectors in R2 on the line y = 5x.

A: Now here,

Q: A Show that the function f: R² → R defined by f(x₁, x₂) = x² + 2x² + 3x₁x₂ + 4x₁ + 5x₂ + 6 is a…

A: Definition of Vector Quadratic Function : Given Function f: R2→R is a vector quadratic function if…

Q: Define a sequence (cn) by n Cn a = 2 (²) ³²+. Σ(2) 3n-k k=0 Find a closed-form expression for Cn.

A:

Q: If X₁ and X₂ are the eigenvalues of A A 30 B 16 C20 D 36 3-1 then X²+ X2 =

A:

Q: Find the limit of the following sequence or determine that the sequence diverges. {((2n3 + n) tan-1…

A: If the limit of the sequence does not exists, we say the sequence is diverges.

Q: For all integers a and b, if 5|(a + b), then 5|(a - b).

A:

Q: Solve the system graphically by graphing two equations on desmos as below: y = 100. ((1+2) ¹20) 12 -…

A: The given equation is, y=100×1+r12120-1r12 and y=20000. It is given graph can be done by using…