Imagine we have a tensor X and a vector Vi, with components 2 0 1 -(:) 1 1 0/ Xij 103 Vi= (-1,2,0). (a) Find the components of XV; (b) Show that XV; transform as a vector under rotation.

Q: Write the vector v = B - 3 8 {[][]}· 8 -2 as a coordinate vector with respect to the basis

A:

Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

A:

Q: Consider the basis B of R² consisting of vectors (-1, 2) and (-6, -3). Find x in R² whose coordinate…

A:

Q: Let F = sin(4x +3z) i-6ye*z k. Calculate div (F) and curl (F). (Express numbers in exact form. Use…

A:

Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

A:

Q: Find the coordinate vector of a = [*]B= -10-30- 2 with respect to the basis B = for R³.

A: Given: It is given that, x→=42-4 and B=152, 01-6, 001. To find: We have to find the coordinate…

Q: What role does the curl of a vector play in an application?

A: We have to write the curl of a vector play in an application.

Q: Find the coordinate vector of = 48 [B = 5 -1 with respect to the basis B = 0 {} for R³.

A:

Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: Find the orthogonal projection of the vector onto the vector .

A:

Q: A vector with magnitude 7 points in a direction 295 degrees counterclockwise from the positive x…

A:

Q: Given u = and V = , find 2u + 3v. O a) Ob) Oc) Od)

A: Given,  u=4,-3v=-1,2 Let's compute  2u=24,-32u=<8,-6> and  3v=3-1,23v=<-3,6>

Q: Identify the type of answer that results from each operation (vector or scalar). If the operation is…

A: