Claim. If r> 1 and 2 E N., then N, - {x} ~ N₁_1. Proof: We have N, - (N-1- {x}) U {x}. Since N, 1- {x} and {x} are disjoint, = N₁ = (N-1- {a}) U{r} = N₂-1- {x} + {x} Since N {x}= = and therefore, N, - {x} ~ N-1. " we have N.1- {x}= , =

Q: (A) List all critical numbers of f. If there are no critical numbers, enter 'NONE'. Critical numbers…

A:

Q: The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal…

A:

Q: btain the general solution to the equation. 1 -23x²y= (529-x²) dy dx y = (23+x)√√529-x² he general…

A:

Q: Let y = 10 U₁ 11 -- and W = Span{u₁} a. Let U be the 2x1 matrix whose only column is u₁. Compute UTU…

A:

Q: Determine whether the function involving the n × n matrix A is a linear transformation.T: Mn,n→Mn,m,…

A:

Q: Find an orthogonal basis for the column space of the matrix to the right. An orthogonal basis for…

A:

Q: A ball is dropped from an initial height of 5 metres. As it bounces, it returns to 80% of its…

A: Calculate the heights of the first three bounces.

Q: Consider the system of linear equations 2x + 7y = 40, 2x - 9y = 110. Write this system in matrix…

A:

Q: Temperature T (°C) 25 20 15 10 5 0 31.5 32.0 1.0230- 1.0235 1.0240 1.0245 B 1.0250 1.0255- $1.0260…

A: Given: The contour plot:To Find:(a) Average rate of change of density with respect to T from B to…

Q: Let A, B, C, D be points such that AB = CD. Prove that {A, B} = {C,D}.

A: As per the question, we have to demonstrate that when the line segment AB is equal in length to the…

Q: Find the equation of the tangent line to the curve given by the equation y = x^3 + 2x^2 - 4x at the…

A: Solution:

Q: Find the general form of the span of the indicated matrices. (Use only x and w as variables in your…

A:

Q: The base of an aquarium with given volume V is made of slate and the sides are made of glass. If…

A:

Q: Solve for y in terms of x, and determine if the resulting equation represents a function. (4y3/2)2…

A:

Q: Let D be an integral domain with unity 1. Two non-zero   elements a,b∈D are associates if and only…

A:

Q: Let G be a group with identity element e. Prove that for any element a in G, (a^2)^-1 = (a^-1)^2.…

A: We are given that G is a group with an identity element e. In group theory, a branch of mathematics,…

Q: Graph the rational function. 6 -2x-1 Start by drawing the vertical and horizontal asymptotes. Then…

A: Given:The rational function is given by .To Find:We have to graph the given rational function.

Q: The ancestors of vertex v are . The descendants of vertex t are . Draw the subtree of the tree in…

A: Let us write the definitions first :An ancestor of a node is any other node on the path from the…

Q: 26. Sketch the region in space bounded by z = x² + y² and z=8-x²-y². Also, sketch the projection of…

A: The given curves are:.To Sketch: (a) Region bounded by both of these curves.(b) Projection of the…

Q: Use Gauss–Jordan reduction to solve each of thefollowing systems. x1 + 3x2 + x3 + x4 = 3 2x1 − 2x2 +…

A:

Q: The principal ideals generated by any two elements of an   integral domain are equal if and only if…

A: We have to prove that the principal ideals generated by any two elements of an  integral domain are…

Q: 3sin x−8sin x−3=0,0sxs2r

A:

Q: Match each of the following with the correct statement. A. The series is absolutely convergent. C.…

A: Give the 6 series,We have to test which series are absolutely convergent , which are not absolutely…

Q: Verify that {u₁.₂) is an orthogonal set, and then find the orthogonal projection of y onto Span…

A:

Q: A factory for the production of electric lamps, consisting of 12 identical machines. Required:…

A: Identical machinesA random sample of  machines is selected.

Q: Find the best approximation to z by vectors of the form C₁ V₁ + C₂V₂. Z= 3 -6 2 3 V₁ 2 1 -2 V2 The…

A: we have to solve the given problem that the best approximation of the z.

Q: Use elementary row operations to transform the augmented coefficient matrix to echelon form. Then…

A: The system of equation:We have to solve the system by back substitution.

Q: Let A a. b. = [22 3 41 2 3 2 1 1 0 00 LO 0 0 1. Find all the eigenvalues of A. Find a basis for the…

A:

Q: Let W be the subspace spanned by u₁ and u₂, and write y as the sum of a vector in W and a vector…

A: Firstly we have to find,

Q: log7(x+1)+ log7(x−5) = 1

A:

Q: y 2x 57. Let T(x, y) = be the temperature at points (x, y) in some region on the plane, and let r(t)…

A:

Q: Write a function in any form that would match the graph shown below. -10 100 80 60 40 20 2 00 8 10 x

A:

Q: First, practice your Taylor Expansion skills by deriving the TE form of sin(x) to the third order.…

A: As per the question, we're asked to first compute the Taylor Series expansion of the sine function…

Q: Use the change of the variables u = x + y √2 and v= y-x √√2 to evaluate -dxdy. 1-xy

A: Given that Let Now,   and  Now, the Jacobian  matrix =

Q: The path r(t) = (t)i + (+²+6) j describes motion on the parabola y=x² +6. Find the particle's…

A: The given position vector is .To Find: Velocity and acceleration vector at t=-3. To Select: Correct…

Q: how did you calculateb the boundaries of the integrals ?

A:

Q: Kk.196.

A: Use the MATLAB ODE45 function to numerically solve the forced Van der Pol oscillator equation and…

Q: Solve by the method of: Solution of ODE by laplace transform y" - y' + 2 y = 4t-6 y(0) = 1, y'(0) =…

A:

Q: Suppose that an satisfies a recurrence relation, and that an is an approximation to an with relative…

A:

Q: Let B = {x² + 2, x² - 4x + 7, -x + 1} be a basis for P2 and let B' = {x³ + x², x³ + x² + x, x+1, x³…

A:

Q: A tank initially contains a solution of 6 pounds of salt in 40 gallons of water. Water with 1/2…

A:

Q: Which chart is easier to understand and why? Item 5 Item 4 Item 3 Item 2 Item 1 02 4 6 8 © 2019…

A:

Q: A. Let V = L(R², R³). Let U = {T € V : T(x, y) = (ax, by, 0) for some a, b ≤ R}. a) Prove that U is…

A:

Q: Use the Root or Ratio Test for these problems. If those tests are inconclusive, only then use some…

A: "Since you have posted multiple questions, we will provide the solution only to the first three…

Q: d²y Find dx² 5x+2y=9 sin (y)

A: Solution:Given: we have to find

Q: Suppose f is a function of two variables given by f(x, y) = 4xy - 2x. If u is a unit vector, what is…

A: To find the largest possible value of the directional derivative Du(1, 3) for the given function…

Q: A 11 1 4-2 4-2 42 -2 0 1 3 Rank is. 0-2 In solving Ax=0, how many parameters you introduces? The…

A: Let,

Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. y + 13 V₂ = 1 6 The closest…

A:

Q: Give a simple condition on r that must be true in order for the following homogeneous system to have…

A: Given system of linear homogeneous equation is following :Thus this system in matrix form is Now if…

Q: Prove that x = 0 is a regular singular point of the given differential equation, then find the first…

A: