Let u (-2, 1), v= (3, 3) and A = = NOTE: Give exact answers. (a) Find ||u|| relative to the inner product on R² generated by the matrix A. || u || 1 1 24 = (b) Find d(u, v) relative to the inner product on R2 generated by the matrix A.

Q: Please show me the steps to solve this question. It is a part of vector calculus.

A: Value of the integral is 9/16Explanation:

Q: Let B={(1,-2,0,-1), (0,1,0,3), (1,2,1.0)], and x=(4,3,-2,-5) Find [x]B Give your answer in the form…

A: B=1, -2, 0, -1, 0, 1, 0, 3, 1, 2, 1, 0x=4, 3, -2, -5

Q: Show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2,…

A: We have to show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v…

Q: Evaulate ∫C▒1/sinzdz , Where C is the rectangle with vertices at -1-i, 8-i,8+i and -1+i oriented…

A: Consider the provided question, The given rectangle with vertices is drawn as,

Q: Given a generic 2x2 matrix A, and a second 2x2 matrix C, show the following: d. Using property c…

A: In this question, concept of matrix operation is applied. Matrix  A matrix is a rectangular array…

Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

A:

Q: True/False: If A is diagonalizable, then so is AT.

A: A matrix is said to be diagonalizable if a matrix of n×n elements has n linear independent eigen…

Q: Current Attempt in Progress Find the scalar triple product u · (v x w). u-(-8,4,4), v- (5,1, - 4), w…

A: Given: u=-8,4,4, v=5,1,-4, w=-7,4,3 To find: u·(v×w)

Q: 3. Let v, and v2 be vectors in an inner product space V. Show that ||v + v2||? < (||Vvl+ ||v2||)?

A:

Q: compute the dot product. (3, −2, 2) · (1, 0, 1)

A: The dot product of three dimensional vectors can be calculated by using the component formula for…

Q: Find the scalar triple product u (vxw). u. (vxw) = u = (-6,1,3), v = (3,6, - 8), w = (-4,3,2)

A:

Q: Find u x v, v x u, and v x v. u = -5i + 3j v = 4i + 5j + 2k (a) u x v (b) v xu (c) V x V

A: The objective of this question is to find the cross products of the given vectors. The cross product…

Q: Is A = diagonalizable. Justify your conclusion. 10 120 -3 5 2,

A:

Q: Find u · (v x w). This quantity is called the triple scalar product of u, v, and w. u = (4, 4, 4), v…

A: = i(5·0 - 0·(-1)) - j (1·0 - 0·0) + k (1·(-1) - 5·0) = i (0 - 0) - j (0 - 0) + k (-1…

Q: The Hamacher product is the t-norm given by ab t(a,b) = a +b – ab Show that this function satisfies…

A: Here the Hamacher product is the t-norm given by t(a,b)=aba+b-ab We have to show that this function…

Q: Solve for the value of x, y, and z using Cramer's Rule 8x +15y + 3z = 143 3x - 7y + 13zi = -62 +…

A: We will find out the required solution using Cramer's rule.

Q: Find scalars x, y and z such that x(2, 1, 4) + y(1,−1, 3) + z(3, 2, 5) = (6,11,6)

A:

Q: Let T (V₁, V2, V3) w = (4, 1, −1). = (2v1 + V2, 2v2 − 3v₁, V₁ — V3). Find T(–4,5,1) and pre-image of

A:

Q: Question Two (a) Prove that the vector field F(x, y, z) = (x² + y²)i – 2y(z+=)j + (zy +2²)k is…

A: The given vector function is, F=x2+yzi-2y(x+z)j+(xy+z2)k. To Prove: this vector field is…

Q: Let x(bar) = (3,-5,2,1,-2) element of R5. Find the norm of x(bar) using the usual norm on R5

A: The norm of x is the distance between a point x to the origin.

Q: Find u x v, v × u, and v x v. u = 2i + 9k v = 4i + 6j – 3k. (a) UX V (b) (c) V X V

A:

Q: 3. Let vi = [1, -2,3], v2 = [-1,–4,5], and v3 = [5,-1,3] be vectors in R³. a) Use determinant to…

A:

Q: a) Find all the real numbers à such the vectors 1- x 1+x and x+1 1 are orthogonal.

A: Two vectors are said to be orthogonal if their dot product is zero. Dot Product There are two…

Q: vectors u and v are such that ||u||=9, ||v||=6 and u*v=-1. Using properties of the dot product, find…

A: Given query is to find the value of the Indicated vector.

Q: T: P2 P₂ defined by T(a + bx + cx2) = a + b(x + 8) + b(x + 8)² Find the following images of the…

A:

Q: Let A = [1 -1 -1              -1   1 -1              -1  -1  1]. Find a diagonalization if possible.

A: We first find the eigenvalues and eigenvectors of A.Start from forming a new matrix by subtracting λ…