al A-[? óJ represents a rotaton transhruntion. b) Let Cl,2,1) be a soluton of the vector equation Xutyx +zW =O, and the matrix A=[u, v, w] represents a linear transtormaton Ti IRR. Then, Nullspace CT) -{83, where O S a zerp vector. is

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of P 1 - b ]

A: Let w= [x y ] is a stable vector of the given matrix.  So, the equations to solve are:

Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

Q: determine if the vector v is a linear combi­nation of th e remaining vectors.

A: Given vectors are Consider

Q: 21. With A as in Exercise 17, find a nonzero vector in Nul A and a nonzero vector in Col A.

A: Given matrix is A=6-4-32-969-6 The column space of A is the space generated by the column vectors of…

Q: Construct the vector 1.1 b+1.5 a having initial point P.

A: Given,

Q: 1.2.4 Prove that vectors (1, 1, 1)", (2, 1,0)", (3, 1, 4)", and (1, 2, –2)" are linearly dependent.…

A: Let v1, v2, v3 and v4 are given vectors that is v1=111  ,  v2=210 , v3=314 and v4=12-2 Claim:    v1…

Q: If a vector space V contains 4 linearly independent vectors, then dim(V) > 4. true false

A: Given ,  If a vector space V contains 4 linearly independent vectors , then  We have to check dim(V)…

Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

A: RECALL: Orthogonal vector:  Let us consider to vectors a→ and b→ then , cross product of a→ and b→…

Q: Prove that the set of vectors B = {(1,2,3), (3,2,1),(0,0,1)} is linearly independent and spans R³.

A:

Q: a. A. vector.orthogenal.tr.Uxv.and.Txw.

A:

Q: determine if the vector v is a linear combi­nation of th e remaining vectors.

A: To determine: Find if v is linear combination of remaining vectors

Q: Find the vector v whose initial and terminal points are given below. (5.5,2.1), (9.5, 6.1)

A: Recall: The vector v with initial point (x1,y1) and terminal point (x2,y2) is, v=x2-x1, y2-y1 We…

Q: () - - (a + bt c+ dt) e *() -- () a (:) - (-) A d - c

A:

Q: O Explatn why each of the followng statements True or False. a) ar[? ó] represents rotation…

A:

Q: Find the coordinate vector of w relative to the basis S = (u1, u2) for R?. Let ui = (5, –3), u2 =…

A:

Q: 1. Find a basis for the orthogonal Conplement of the Subs pace of IR? Spanned by the vectors…

A:

Q: 6) a) Express the vector (8,0,5) as linear combinations of u (1,2,3), v = (2,-1,1), and w (0,1,4)

A:

Q: Find the scalar and vector projections of b onto a, where a=⟨−1,1,2⟩ and b=⟨−1,5,4⟩

A:

Q: 8.) find a vector of norm 2 that is orthogonal to the three vectors, u=(2,1,0), v=(-1,- 1,0) and…

A: Just assume a vector and apply criteria of perpendicular of two vectors ..as I have done solution in…

Q: Find the length of the vector. v = (-2, 0, 5, 1) %3D ||| M = %3D

A:

Q: 11) in triple cross of vectors (A × C) × B = Cx (B × A).

A:

Q: #15. aib are liearly indepandant vectors in IR? Let F= Span faib, 2ar3b}. Then the dmensian of A) I…

A:

Q: Decompose the vector ¯b = ⟨1, 0, 4⟩ into its projection proja¯(¯b) and its orthogonal component…

A:

Q: Find the scalar and vector projections of b onto a. a = (4,7,-4) b =(4,-1, 1)

A:

Q: what is the terminal point of a vector with initial point that Ar (-1,0is equivalent to u 3,4 O B3)…

A:

Q: -2 Show whether or not the vector bs is a linear combination of the vectors a, = az = and az = that…

A:

Q: Determine whether each collection of vectors is linearly independent or linearly dependent. Justify…

A:

Q: Find a vector that is orthogonal to both v = (1, –2,3) and w = (2, 1, –1).

A:

Q: a. Please provide a well explained answer for the follwoing. And explain what are the components of…

A: Components of vector  In two dimensional ,any  vector can divide into two components x -…

Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

Q: Prove that a·a= = |a|2, where a is a vector with n components

A:

Q: . Prove that (only one): E - 4y-V3ay is a unit vector? a- F 2 b- A = 6ax - 3a, + 2a, and B = 3a, +…

A:

Q: Find the scalar and vector projections of d = (4, 2, –5) on b = (3, –1, 6).

A:

Q: 19. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1, –4,0), v = (-1,–1,2,2),…

A: Step:- 1 Given that u=2, 1, -4, 0,  v=-1, -1, 2, 2,  w=3, 2, 5, 4 Now, first we check the given…

Q: The set of vectors u = , and u2= are having rank 3 having rank 1 Linearly independent Linearly…

A:

Q: 10) (6 points) Using the inner product (v, w) = 3v¡W1+5v2W2 with the vector space R?. a) Find a…

A:

Q: 9) Suppose {v,V,v, } is a set of linearly independent vectors of a vector space V. a) Is {v,v +v, v,…

A:

Q: the norms of a vector X = [1,12, ...,I" and matrix A = (a5) are respectively defined as ||X|| = E…

A: Given, the norms of a vector                     X=x1, x2, . . ., xnTand matrix…

Q: Construct the vector 1.4 b+1.7 a having initial point P.

A:

Q: determine if the vector v is a linear combi­nation of th e remaining vectors.

A:

Q: Show that if C is any two-dimensional vector then it can be written as a linear combination of the…

A: Given: C→ be any two dimensional vector spaceie.,   C→=x,y|x,y∈ℝFormula: Convex set∃ t,s∈ℝ such that…

Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…

A:

Q: 1] Suppose that W, N are non-zero two- dimensional vectors which are not parallel. Show that if C is…

A: We have to solve given problem:

Q: Compute the projection of →a→ onto →b→ and the vector component of →a→ orthogonal to →b→. Let…

A:

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of 1 - a а P = 1 - b [ W =

A:

Q: A set of vectors S={v in a vector space is called linearly independent if the vector equation c…

A:

Q: 9. Determine if the vectors å = [-1, 2, 1], b = [-2,4, 2], and ở = [12,8, 1] are coplanar. %3D

A: given vectors a=[-1,2,1] b=[-2,4,2] c=[12,8,1]

Q: Find a unit vector that is orthogonal to both u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩.

A: The given vectors are u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩. Compute the cross product of u and v as…

Q: 6. Find a unit vector that is orthogonal to both [0, 1, 1] and [1,0, 1].

A: We will find the unit vector orthogonal to both the vectors as following.

Q: Let a = (4, 8, -6) and b = orthogonal to a. (2, 2, –7) be vectors. Decompose the vector b into a…

A: We are given a=(4,8,-6) and b=(2,2,-7) be the two vectors. We have to decompose the vector b into a…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.