Refer to P, with the inner product given by evaluation at - 1, 0, and 1. Compute (p.a), where p(t) = 5-t, q(t) = 6 + 512. (p.4) =O

Q: Consider the following inner product R?. on ((T1. Yı), (T2. Y2)) = ax122 + by,Y2 If ||(1, 3)||² =…

A: We will find out the required value of a+b.

Q: Show that the function a Y1 (x, y) = [21 2] в с Y2 is an inner product on R? if and only if b2 – ac…

A:

Q: For z € C, define Tz: CC by Tz(u) = zu. Characterize those z for which Tz is normal, self-adjoint,…

A: Given that: For z∈C, Define Tz:C→C by Tzu=zu. The objective is to verify the given statement. Now…

Q: Find the first piece S1 (x) of a natural cubic spline that interpolates the set of points (0,1),…

A: Formula for cubic spline interpolation is…

Q: Find the Ker(T) and Rng(T) and their dimensions. T:R → R defined by T(x)= Ax , where 1 -1 A = -3 3…

A:

Q: Find –3xyd A over the D triangular region D with vertices (0, 0) (2, 0), (0, 4)

A:

Q: 9. Show that the function (-, -) : IR² × R² → IR defined by setting = #1#2 + 2x12 + 2y1*2 + 8y1Y2 /2…

A:

Q: Consider P with the standard inner product. Then which one of the following pair is orthogonal a)…

A: P2 is the space of all polynomials of order ≤2. The standard inner product is defined as dot product…

Q: verify that (A + B)T = AT + BT

A:

Q: Consider P2 with the inner product (p, q) = | p(x)q(x) dx . Let U = span{1,2x + 2} and g(x) = 3x? +…

A: Consider P2 (polynomials of degree atmost 2) with the inner product defined as follows, p, q=∫-11…

Q: Consider P2 with the inner product (p, q) = | | p(x)q(x) dx . Let U = span{1, 2x + 2} and g(x) = 3x2…

A: See the detailed solution below.

Q: Let yk = k² and Zk = 2k|k|. Are the signals {yk } and {Zk } inearly independent? Evaluate the…

A:

Q: Let Ps have the inner product given by evaluation at-2,-1, 0,1, and 2. Let p(t) = t2- 2t and q(t) =…

A: Let P3 have the inner product given by evaluation at -2, -1, 0, 1 and 2 . Let p(t) = t2-2t  and q(t)…

Q: * Consider a piecewise linear interpolation of exp(x), O<=x<=2, with h=0.01; that is, split [0,2]…

A:

Q: Find the characteristic of Zm, × Zm, × · · × Zmr where m;'s are positive integers.

A: The ring ℤm1×ℤm2×...×ℤmk is a ring with unity 1,1,1,...k times Now, to find characteristic of…

Q: Consider P2 with the inner product given by evaluation at - 2, 0, and 2. Compute ||p|| and |q| for…

A: In this question, concept of inner product is applied.

Q: Let D be the portion of z = 2x + 5y inside x² + y² = 1, oriented up, and let F = (3, 2, -2). Compute…

A:

Q: Which of the following points are collinear to (1,0) and (3,6)? Show graphically and analytically.…

A:

Q: 3. Find the generator of Xt = Xo + ut + oWt, where W is a standard BM, and identify the PDE…

A: 3).

Q: where A e C.

A: Complex Inner Product Space: For two vectors u and v in complex space ℂn, u,v is known as complex…

Q: The area bounded by the curve y = 7x and the lines z= 2 and =9 above the z-aris is O 539.00 square…

A:

Q: Consider P2 with the inner product given by evaluation at - 2, 0, and 2. Compute ||p|| and ||q|| for…

A:

Q: Find the decomposition of a(t) a = arT + așN into tangential and normal components for r(1) = (5t,…

A:

Q: Consider P2 with the standard inner product. Then which oe of the following pair is orthogonal a)…

A:

Q: Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.

A: fx, y=x2y2 Partially differentiating with respect to x, we get ∂f∂x=2xy2 Partially differentiating…

Q: and w = x.+ 2y. y 3. Compute the inner product g (v,w) of v = . + x. ay' 2 дх ду дх Where the line…

A:

Q: Compute the Wronskian, W[y1, y2](t).

A: Let y1(t) and y2(t) be two differentiable functions in the independent variable t. Then the…

Q: find an antiderivative Fon of the function fox)=5sinX such that FCO)=1.

A:

Q: Consider P2 with the standard inner product. Then which one of the following pair is orthogonal a)…

A:

Q: Given: PT || QS a. Prove: APRTO AQRS R T. b. What similarity transformation maps APRT onto AQRS?

A: Corresponding angles are the angles that are formed when two parallel lines are interested by a…

Q: Let D be the portion of z =2x+5y inside x2 + y2 = 1, oriented up, and let F = yi + zj – xk. Compute…

A:

Q: Evaluate z'dz where C is z=2 by Residue theorem. (z-1) (z-3) (s-2) ,(1-2)}

A: Given A complex integral we can use cauchy's residue theorem to solve the problem

Q: For z ∈C, define Tz: C →C by Tz(u) = zu. Characterize those z for which Tz is normal, self-adjoint,…

A: Firstly, find out Tz*.

Q: Define T:R → R' by T(x, y, z) = (x-5y+4z, y- 6z). a) Is T one-to-one? Justify your answer. b) Is T…

A:

Q: Consider P2 with the standard inner product. Then which one of the foilowWing pair is orthogonal a)…

A: We are given: Inner product space P2 with standard inner product To find: which pair is orthogonal

Q: Find the Ker(T) and Rng(T) and their dimensions. T:R →R defined by T(x)= Ax, where 1 -1 27 -3 3 -6

A: The objective is to find ker(T) and range (T) and their dimension.

Q: Let, T: R3 → R³;T(x, y, z) = (2x + y, y – z,2y + 4z) Find the rank and nullity of T.

A:

Q: Evaluate the following. 5y + z S: z = 15 - 6x + 8y, 0 < x < 1, 0 < y < 3

A:

Q: Find the area inside the inner loop of r = +5 12cosθ .

A: Given equation as r=5+12cosθ

Q: Consider P2 with the inner product = f (x)g(x) dr. Then d(x, 2) Jo

A: d(x,2) represents distance between the vectors x and 2 P2 is the set of all polynomials with degree…

Q: O8.D. If w, and w, are stri (x, X2) -(y Ya) = x,y,W,+Xay,W, uinlde an inner product on R'.…

A: 8.D  Let w1 and w2 are strictly positive i.e. w1,w2&gt;0.(x1,x2),(y1,y2)∈ℝ2Define the product…

Q: Find det (T) for T:R- R, where T(x,,×2,*3) = (x,- x2, X2 - X3, X3-x).

A: We will find the matrix [T] from the image of the standard basis vectors of R³ under the…

Q: 3. Show that à = (6xy + z³)î + (3x² – z)ĵ + (3xz2 – y)k is irrotational. Find p such that A Vọ.

A:

Q: Let P2(R) have the inner product, (p, q) = f* p(x) q(x) dx, Vp, q € P₂ (R). Find the best…

A:

Q: Find the cemplex fourth routs of Z: 2 J3-22

A: Given, z= 2√3-2i Therefore, r= √[(2√3)²+(2)²] r= √(12+4) r= 4 θ= tan-1(-2/2√3) θ= -30°

Q: In C[-1,1], with the standard inner product f(x) = e² and f(x) = e ² are orthogonal. %3D O True O…

A: Given- fx=ex and gx=e-x. To Check- If the given functions with the inner product are orthogonal or…

Q: Fit a quadratic function of the form f(t) = co + Ct + czť to the data points (0,0), (1, 12). (2, 6).…

A:

Q: In C[0, 27], with the inner product -2 (f, 8) = | f(x)g(x) dx, show that the set S = {1, sin x, cos…

A: Given: Inner product defined as: &lt;f,g&gt; = ∫02πf(x)g(x)dx To show that the set S = { 1, sinx,…