show that the scalar t that minimizes ||y– tx||

Q: Calculate F. dĩ, where C is the square of (1,1, 1), (–1, 1, 1), (–1, –1,1) and (1, –1,1), with…

A:

Q: Let A - ( ) a. Show that the vectors lz.A, A² are linearly dependent in Maz (R). b. Deduce that A"…

A: Statement (S1) proves that  I2 , A, A2  are linearly dependent.

Q: Determine a scalar s such that A2x = sx when Ax = rx.

A: To determine a scalar s such that A2x=sx when Ax=rx Given Ax=rx On multiplying both the sides by…

Q: Find a norm of the function f(t) = t² in space C" 0, 1, where norm is given by formula max|f(t)|+…

A: Solution

Q: 2) Let f(x,y,z) =x²y³z* Use the Lagrange multiplier method to find the maxi- mum value of f on the…

A:

Q: Find the linearization L(x) at x= a. f(x) = x+ a = - 1

A:

Q: Show that the vectors (3+ /2,1+V2) and (7, 1 +2\/2) in R² are linear!ly dependent over R but…

A:

Q: Fit a quadratic function of the form f(t) = co + ct + czť² to the data points (0, 0). (1, 12), (2,…

A:

Q: suppose Vn is the vector space of polynomials of degree <n-1 and with real cofficients. Determine…

A: As per the question we are given a vector space Vn of polynomials with degree ≤ n-1 and with real…

Q: Enter the function In standard form. y = 2(x-1)(x +5) The standard fom of y = 2(x-1)(x +5) is

A: y=2(x-1)(x+5) first multiply (x-1)(x+5) =&gt;(x-1)(x+5) =&gt;(x^2 +5x -x -5) =&gt;(x^2 +4x-5)

Q: Show that: (a) Cov(X,Y) = E[XY] – E[X]E[Y]. (b) If X and Y are independent, then fY|X(y|x) = fY(y)

A: Solution:a.Show that COV(X,Y)=E(XY)–E(X)E(Y)

Q: Consider the vector-valued function [f(x, y) xt – xy² [g(x, y) 2 Vx + y³x² [f(x, y) Which of the…

A: Find the Jacobian of the given matrix

Q: Let ū = (u1, u2) be a unit vector in R? and let f: R² → R be defined by if (x, y) # (0, 0), f (x, y)…

A:

Q: Q1) Use a suitable Linearization to find the best fit of the form f(x) = Cx3 + for the %3D data:…

A: Given the data,                 (1, -1), (2, 7), (3, 26.3)

Q: 14 Verify the given linear approximation at a = 0. Then deter-

A:

Q: If a € RN and oTax ≤ √√₁9² * V vector. (a) maximize or such that (b) maximize ar such that (c)…

A: Given below clear explanation.

Q: Use the least squares method to fit a curve f(x)=ax² + b TO THE POINTS EMPIRICAL (0,1.1), (1,1.7),…

A: Given the points empirical  (0,1.1),  (1, 1.7),  (2, 5.2) We need to fit a curve fx=ax2+b using…

Q: Suppose F (x, y) = (2xe-", 2y – a²e="} (a) Find a scalar function f (x, y) such that F = Vf (b) Use…

A:

Q: Determine a scalar r such that Ax = rx, where 1 A =| 1 1 and x = 4 -4 5

A: Ax=r x ⇒ x is an eigenvector of Afor the eigenvalue r. So to find r, we compute all the eigenvalues…

Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

A:

Q: [#1] Exercise 7.46. Prove that if y = y' then y = ky' for some scalar k.

A: Given that γ≡γ' The y can be written as,  γ≡r mod n The y' can be written as, γ'≡ r mod n

Q: Determine if the functions Y1=e^{4x}senx and Y2=e^{4x}cosx are linearly independent or linearly…

A:

Q: Show that the function f(x, y, 2) = (x² + y² + 2e**)4 is strictly convex on R³.

A:

Q: Consider the bounded linear operator T:C0,1]C0, 1] defined by -Ta =y y(t) = ta(t). Enter the norm of…

A: Given that T:C0,1→C0,1 is a bounded linear operator. Defined by x↦Tx where x is continuous function…

Q: Determine a scalar r such that Ax = rx, where

A: Matrix: A=12-11014-45x=-12141AX=12-11014-45.-12141

Q: ey are linearly dependent, find scalars a, b, and c, not all zero, such that au + bv + cw = 0 u =…

A:

Q: Find the residues of f(z) = z²-2z (z+1)²(z²+4) at all its poles in the finite plane.

A:

Q: In the vector space of all real valued functions, find O (1+cos 2t, cost sint, cos² t) O (sin 2t, 1+…

A: Given spanning set is sin 2t, 1 + cos 2t, cos t sin t, cos2 t

Q: 4. Show that the norm on l0 given by I| (11, .., In...) |lo= sup{|r;| : j= 1,2, ...} can not be…

A:

Q: Find the maximum modulus of the function f(z) = -iz + i, |z| < 5.

A: Find the maximum modulus of the functionfz=-iz+iz≤5

Q: Determine a scalar s such that A2 x = sx when Ax = r x.

A: Given that Ax=rx. Multiply both sides of the above equation by A and simplify as follows.

Q: If f(x) and g(x) have a period p, show that h(x)3Da f(x) + b g(x) (a, b constants) has the period p.…

A:

Q: Determine a scalar r such that Ax = rx, where 1 A = and X=

A: Given, A=2112, x=11

Q: suppose that x,y,z∈R3 are such that x.(y×z)≠0. prove that x,y,z are linearly independent.

A:

Q: Let f1(x) = 3x and f2(x) = ∣x∣. Graph both functions on the interval −2 ≤ x ≤ 2. Show that these…

A:

Q: Fit a quadratic function of the form f(t) = co + cit + czť² to the data points (0, –6), (1, 2), (2,…

A:

Q: 1. Use the Wronskian to show that the functions are linearly independent. Yı = e*, y2 = e2*, y3 =…

A:

Q: Let C be the rectangle in the xy-plane with vertices (0,0), (1,0), (0, 2) and (1, 2), and let F(r,…

A:

Q: Find the linear least squares polynomial approximation to f(x) on the indicated interval if a. f(x)…

A:

Q: Let r; = ro + hj for j = 0,1,2. Use the quadratic polynomial interpolating f at those nodes %3D %3D…

A: The solution is given below

Q: Show that if k is a scalar and A is n × n, then det(kA) = kn det(A).

A: Show that if k is a scalar and A is n × n, then det(kA) = kn det(A). For any scalar k, we need to…

Q: Fit a quadratic function of the form f(t) = co + cit + czť² to the data points (0, 1), (1, –7),…

A:

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: Let T: 1 1 be defined by (1, 62, E3,) (0, 0, 6, E). Is T bounded? Self-adjoint? Positive? Find a…

A: As this is a multiple sub-part question, according to the Bartleby Answering Rule, only first three…

Q: Use the inner product 1 (f, 8) = f(x)g(x) dx in the vector space CO[0, 1] of continuous functions on…

A:

Q: Letf(z) 3z-2i. Find the maximum valne of /(=} on the disk z<.

A: Triangle inequality:z1-z2≤z1+z2 and z1+z2≤z1+z2

Q: d) must be done using Vector Calculus and the Lagrange multiplier. Optimize: the function f(x, y) =…

A: Given: The function fx,y=49-x2-y2 subject to the constraint x+3y=10. To optimize the function we'll…

Q: Consider the vectors x"(t) =( t and x (t) = ( 4t 6. (a) Compute the Wronskian of x) and x2). (1) W =…

A:

Q: Fit a linear function of the form f(t) = co +ct to the data points (-2, –14), (0, 10), (2, 22),…

A:

Q: Determine a scalar r such that Ax = rx, where

A: