Prove (A = B) = (A v C) = (B V C)

Q: prove thats. u.w V.W V.

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Q: Consider the collection of vectors --000 1 Is Slinearly independent? Carefully explain your answer.

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Q: find ---y (a) u•v, (b) u•u, (c) ||v ||2, (d) (u• v)v, and (e) u • (3v).

A: Disclaimer: Since you have asked a question with multiple sub-parts, we will solve the first three…

Q: Use Cramer's rule to fins a solution: 3x-2y=4 6x-4y=0

A: Cramer’s rule:

Q: What must be value of X so that B is diagonalizable?

A: A matrix A can be diagonalized if there exists an invertible matrix P and diagonal matrix D such…

Q: AB is orthogonal

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Q: А Q(1, 1) в Q(2, 0) vyQ(1, y) 3xQ(x, 2)

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Q: Show: Cov (X,Y) = E[X(Y – μY)]

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Q: Prove that: V² (64) = $V²y +2V¢• Vy+yV² ¢

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Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3u + 2x = w − v

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Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: Show that (u×v)· w = u ·(v×w).

A: As we know that, Multiplication is an Associative Property, i.e. (a x b).c=a.(b x c) and Sometimes…

Q: (d) u =-,v = xy, = a' ху, 21

A: Consider the given information. (d) Consider the given values. u=12-12x2v=xy The equation of the…

Q: Let u, EC prove that ū · v = v · ū น

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Q: Use Cramer's rule to solve for r' and y in terms of x and y: y = 31' – 2y

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Q: Show that (u - v) × (u + v) = 2(u × v)

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Q: Determine whether X and Y are independent: 2e--2y x, y > 0 a. fxy(x, y) =

A: Hello! As you have posted 2 different questions, we are answering the first question (4-2). In case…

Q: How do you know if 3 vectors span R^3? Is there any example?

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Q: T: R2 R2 is defined by х + 7х, [3x, – 4x2] X1 %3D and B = {u,,u,} and B' = {v,v,}, where %3D -- --…

A: Given transformation T:R2→R2, defined by Tx1x2=x1+7x23x1-4x2 and B=u1, u2 and B'=v1,v2 Here u1=22,…

Q: Verify f U= n1 V = 234 43 snyz %3D +23- 422-24-42- dependend %3D fundlarelly are

A: We know the identity: x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx) --(1) We are…

Q: Solve using Cramer's rule. 2x+8y = 11 4x+6y = 3 %3D %3D

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Q: Show that Plx-1,y) = A(x, y) X+ y-1

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Q: Use the result of Exercise 41 to show thatf1−α,ν1,ν2 = 1fα,ν2,ν1

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Q: Find ||u||, ||v ||, and ||u + v||. -(-1. 금), v-(2.-3) v = (2 - ± ) u = 4 (a) ||u|| (b) ||v|| (c) ||u…

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Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: 5. What is UF, where F = 0? Prove the correctness of your %3D answer / computation.

A: To find- What is ∪F, where F = ∅? Prove the correctness of your answer/computation.

Q: Prove u + v = (u + v)(u* – u³v+ u?v² – uv³ + v^). + u-v - U (u+ v) (u+ – u³v+ u²,2 – uv3 + v^) Enter…

A: We have to prove: u5+v5=u+vu4-u3v+u2v2-uv3+v4

Q: Solve Ut = Urx, x > 0, t> 0, u (x, 0) = f (x), u (0, t) = 0.

A: Given partial differential equation isut=uxx,     x>0,     t>0ux, 0=fxu0, t=0

Q: What is the resulting diagonalized

A: A quadratic form may be diagonalized by the following procedure: Find a variable x such that x2…

Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: Use Cramer's rule to solve for x, y and Z 2х + у — 3z %3D 0 | 4х + 5y + Z %3D 4 %3D

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Q: Prove that this argumentation is valid Vx. 3y. A(x, y) - Vx.3y. B(x, y) 3x. Vy. ¬B(x, y) : 3x. Vy.…

A: Given: An argument…

Q: Find u · (v x w). u = 2i – 3j + 4k,v = 9i + 2j – 5k,w = 4j + 6k u · (v x w) :

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Q: |(u+ v) x (u – v)I = 2|u x v|

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Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R3 if x = [1,-2,4] and…

A: Cauchy schwarz inequality -  For any vectors u and v in an inner product space V,  |<u,v>|…

Q: Prove that u × (v + w) = (u × v) + (u × w).

A: Here the objective is to prove that

Q: Prove that dv du 2 – u? + v² 18

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Q: Find v−w​, if v ​= −3i +6j and w ​=-5i+5j IIvII-IIwII=?

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Q: Prove that jer² √ d dx = 2

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Q: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

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Q: Show that u and v are orthogonal if and only if ||u + v||² = ||u||2 + ||v||². (Please avoid an…

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Q: Use Cramer's rule to solve for z. Зх — 4у + z %3D 3 2х + 3у = 8 5y + 8z = 11

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Q: prove using soundness that the converse of Axiom 2: (vx)A → A[x := t] is not a theorem

A: Solution: If Î" ` Ï• then Î" |= Ï•. Completeness If Î" |= Ï• then Î" ` Ï•. Thus, any formula proved…

Q: Prove that −(−v) =v

A: To prove: --v=v

Q: Prove Equationally that A, B H A = B.

A: Given:                       A, B ⊢ A≡B To do: Prove the given statement equationally.

Q: 6. Write as a linear combination of the vectors

A: solving by linear combination of the given three vectors by converting into syatem of equation...

Q: what Is the v product of two vectors a=C1,4)-2),

A: Which is a scalar quantity.

Q: Find Cov(X, Y)

A: Covariance: It is a statistical measure used to establish a relationship between two random…

Q: If A has two orthogonal columns each of length 6. Then A^TA is equal to

A: See the attachment