Suppose ū = (-3, -5,–2) and ī= (0,0, –4). Then: (1) The projection of ū along v is (2) The projection of u orthogonal to V is

Q: Suppose that v1,..., Um is linearly independent in V and wE V. Prove that dim span(v1 + w,..., Vm +…

A: Let u1,u2,⋯,un be a set of vectors in a vector space V. This set of vectors is said to be linearly…

Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: If |r(t)| = c (a constant), then r' (t) is orthogonal to r(t) for all t.

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Q: A linear transformation T: R → R? is given as 1 2 3 1 0 1 Y1 T: = Y2 Find all vectors 7 E R³ such…

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Q: Find the projection of u along v. u = 5i + 7j − 4k, v = k

A: Given, u = 5i + 7j − 4k, v = k To find the projection of u along v.

Q: find the distance d(u, v) between u and v in the given exercise.

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Q: The vector v with initial point (0, 0) is shown below. Write v in the form v = ai+bj, where a and b…

A: It is given that initial point of vector v is (0,0). The objective is to write vector v in the form…

Q: The orthogonal projection of v = 10i on b = −3i + j is _____ .

A: To find the orthogonal projection of v = 10i on b = −3i + j .

Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

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Q: Let E The orthogonal projection of y on H = span{ u 1, ú 2} is given by:

A: Given

Q: Let x = (1, 1, 1, 1)T and y = (8, 2, 2, 0)T . Verify that x − p is orthogonal to p.

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Q: Find u × v and show that it is orthogonal to both u and v.u = (−2, 1, 1), v = (4, 2, 0)

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Q: Find u × v and show that it is orthogonal to both u and v.u = (2, −3, 1), v = (1, −2, 1)

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Q: Consider the following. (4,-1, 0) 7, 0) Find u x V. Determine if uxV Is orthogonal to both u and v…

A: We have given  u=⟨4,-1,0⟩v=⟨-4,7,0⟩ Then, u×v=ijk4-10-470=i0-0-j0-0+k28-4=24k

Q: Find the orthogonal projection of y onto u 16 8. 48 OA. 32 4 OB. OC. OD. 32 - 16

A: We have to find orthogonal projection of y onto u

Q: Which of the followings is the vector projection of u onto v where u = -2i + 4j – V5k and v = 2i –…

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Q: Find u × v and show that it is orthogonal to both u and v.u = (1, −1, 1), v = (0, 1, 1)

A: Cross product is,

Q: Find the orthogonal projection of y onto u. y = -3/5] - 4/5 /5 4/5 b) c) d) 2.

A: The formula to find the orthogonal projection of y onto u is: projuy=u→.y→u→2.u→ Here,…

Q: Find the orthogonal projection of y onto u. - 8 4 y = u: 6. 12 O A. 1 4 3 4 О В. 4 12 Ос. 16 48 O D.…

A: We have to find orthogonal projection of y on u.

Q: Given vector u = (-1, –1) and v = (-1,1) , determine the value of 5v – u in component form.

A: A vector is a quantity with magnitude and direction. Given a coordinate system a vector can be…

Q: Given v = (8, –3) and w = (12, -4), find vector projection of v onto w.

A: Solution; Consider the given vectors :  v = 8, -3 and w = 12, -4 Now, vector projection of v onto w…

Q: Find u × v and show that it is orthogonal to both u and v.u = (−1, 1, 2), v = (0, 1, −1)

A: Given vectors

Q: Find u × v and show that it is orthogonal to both u and v.u = (1, 1, 0), v = (0, 3, 0)

A: We have given; u = (1, 1, 0), v = (0, 3, 0)

Q: Find the orthogonal projection of y onto u. y = ,u = -3%5) b) c) d)

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Q: Find u × v and show that it is orthogonal to both u and v.u = (4, 1, 0), v = (3, 2, −2)

A: Now cross product is,

Q: If F.T ds = 0, then F and T are orthogonal. %3D C O True False

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Q: In R, evaluate the alternating 2-form 5 = -3 · dx A dy on the pair of vectors (a, b) if a = (4, 2,…

A: In ℝ3, we have to evaluate the alternating 2-form ξ=-3·dx∧dy on the pair of vectors (a,b). a=4,2,12…

Q: The vector v with initial point (0, 0) is shown below. Write v in the form v = ai+bj, where a and b…

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Q: Compute the orthogonal projection of i = onto the line L through and the origin. proj, (1) =

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Q: Let u = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that u + v and w are…

A: Here, u=(1,2,3,4),v=(02,t,3) & w=(1,1,0,1)

Q: If u = x²+2x-y and v = - 2xy - 2y, then the vorticity vector is - 3yk 10 -yk 1O IIO yk IIO

A: Given u=x2+2x-yand v=-2xy-2y

Q: d) Find the orthogonal projection of v = 1 into U+. (1)

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Q: The projection of v onto w is v=i+j+2k, and w=i+2j+2k 3 =(-i+j+2k) а. (i + 2j +2k) 5 -(i + 2j + 2k)…

A: Projection vector of a⇀ on the b→ is given by c→=a→·b→b→b^

Q: For which value of x do the following vectors form a linearly dependent set in R V =| x, x,

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Q: Suppose T: R³ → R² is a linear map and that u and v are particular vectors in R. If T(u) = (2, –3)…

A: Given query is to find the indicated vector.

Q: In R, evaluate the alternating 2-form 5 = -3· dx A dy on the pair of vectors (a, b) if a = (4, 2,…

A: Given that, ξ=-3.dx∧dy on (a,b) Where a=(4,2,12),b=(-7,-4,8) The objective is to show that ξ(a,b).

Q: Find a nonzero vector u with initial point P(-1, 3, -5) such that u has the same direction as v =…

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Q: If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:

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Q: Consider the sets of vectors  S={u,v,w} and T={u,v,w,x}. Which of the following is true:  -If T is…

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Q: In R', evaluate the alternating 2-form 5 = -3 · dx ^ dy on the pair of vectors (a, b) If %3D a = (4,…

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Q: The vector E = = -a, – 4as + 3a, expressed in RCS and in terms of ø is Е 3 (-сosф + 4sinф)ax +…

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Q: Consider the vector-valued function F(2,) = [xy² + 2ye* х, у y 3xe-y Which of the following are NOT…

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Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w?

A: x is orthogonal to v and w. Then their dot product is zero. That is, ⇒x·v=0  &  x·w=0

Q: Let P = (-2,0, 5), Q = (3, 1, 1), and R = (0,0, 4) and define a = PQ and b= PR. Find %3D (c) The…

A: To obtain the vectors a=PQ→ and b=PR→, find the differences of the points P, Q and P, R,…

Q: The orthogonal projection of v = 10i on b = –3i + j is <

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Q: Find u × v and show that it is orthogonal to both u and v.u = (12, −3, 1), v = (−2, 5, 1)

A: Given vectors u=12,-3,1v=-2,5,1 Their cross product is u×v=ijk12-31-251…

Q: (1, 2, 1) on to the line x = 2+ t, y = 3 – t, z = t. Also Find Find the Projection of b = Projection…

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Q: Let B= { }],19} be basis for IR. %3D Find [v]g where V= 15

A: Given :                          Basis  B = 3-30, 22-1, 114 and V = 15-93…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.