Let P be a projection of a normed lined

Q: Can any of the given sets of 3-vectors below span the 3-space? Why or why not? (a) [121] [231] [342]

A: The given vectors are (1 2 1) , (2 3 1) & (3 4 2). We have to check whether they span the…

Q: Show that the list of vectors {r + 2, x² + 2, x³ – 3, x4 – x² + 1} is a linearly independent set of…

A:

Q: The vector projection of M = 2ax + 3ay + 2az onto P = 3ax + 2ay + 3az is

A:

Q: Find the projection of (1,2,3) onto (a,3,7)

A:

Q: (i) Compute the vector projection of u onto v, proj u , where V u = (3, 3) & v= (2, 0). (ii) What is…

A: The given vectors are u=3,3 and v=2,0

Q: Which of these are linear subspaces? :2x +3y=D0}in R? :xy: A. Is a linear subspace ):v = 1– x}in R?…

A:

Q: Show that W is a vector space.

A:

Q: Find the projection of u = onto v = .

A:

Q: Find the projection of u = onto v = . projuv =

A: We can find the projection in two form one is in scalar form and other is vector form. here i give…

Q: Solve the system of linear equations Зх, — х, %3D2 X, +4x, = 5 using Jacobi iterative method with an…

A: We have to use the Gauss Jacobi iterative method to perform iterations for the following linear…

Q: The shape's vector set is a subspace of R3

A: solution :-

Q: (b) (x1, Yi, Z1) + (X2, Y2 Z2) = (0, 0, 0) c(x, y, z) = (cx, cy, cz) O Thể set is a vector space. O…

A: b. A set S is said to be a vector space if for any vectors a,b in S and scalars s,t, as+bt belongs…

Q: What is the dimension of the vector space P°?

A: The dimension of Pn is n+1

Q: if u = <1,-3,1> and v = <2,2,2> then find the projection of u onto v

A: The objective of this question is to find the projection of vector u onto vector v. The projection…

Q: Give examples of two sets of vectors in P3 such that one of them is linearly independent and another…

A:

Q: 2. Let W1 and W2 be two subspaces of V, such that dimg(W1) = dimg(W2) = 2. Suppose that the only…

A: here we can use linear combination to prove that given set is linearly independent.

Q: d) The set of real numbers, with addition defined by x + y %3D х - у

A:

Q: Suppose we have a set of vectors v_1...v_n such that v_1 could be written as a linear combination of…

A:

Q: Suppose that u = (0, 1,-2) and v = (1, 0, 1). Compute the projection of u onto v. Enter the…

A:

Q: 1 1 -1 Let S ). Determine the dimension of the span of S and which vectors can serve as a basis for…

A:

Q: Show that span(S) = span(S U{0}). That is, by joining or deleting the zero vector from a set, we do…

A:

Q: If on V = R² define the usual scalar multiplication « (x, y) = (« x,x y) , and addition (x1, Y1) +…

A: Concept: Vector space: Vector space is defined by the associative and commutative laws of vector…

Q: 0 0 0 0

A:

Q: Find the projection projuv, where u = (1,3,-2) and v = (2,-1,3).

A: Since we kow that the projection of v on u is given by                projuv=u.v||u||2u

Q: Suppose there is a collection of three or more two- dimensional vectors. Provide an argument…

A: Collection of two dimensional vectors mean those vector having i and j components.

Q: Prove that if T is diagonalizable then T is diagonalizable.

A: Let V be a vector space of dimension nand T:V→V be a linear transformation such that T is…

Q: Let S be the parallelogram then determine the area of parallelogram by the vectors [h and b2 h/2 [1…

A: The parallelogram is determined by the vectors  b1→=hh2=10251                              (since…

Q: Look for or create your own set W that is a subspace of R' or R.

A: We create a subspace of ℝ3.

Q: Let x = (1, 1, 1, 1)T and y = (8, 2, 2, 0)T . Find the vector projection p of x onto y

A: the vector projection in the direction of another vector is the orthogonal projection of a vector…