Which of the following are always true, and which are not alwaystrue? Give reasons for your answers. u * (v + w) = u * v + u * w

Q: Let [1 2 21 A = 1 1 -1 0 and U = |-2, then determine if 3 -1 2 (i) U is in Nul A. (ii) U is in Col…

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Q: 3 Let vį = . If u 1 vị and ul v2, then y = -1 -2 a) -9 b) -8 c) 10 d) 9 e) 7

A: We use the definition of perpendicular vectors to find the value of y.

Q: Determine whether the statement is true or false " If u ∙ v = u ∙ w and u ≠ 0, then v = w", If it is…

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Q: 3. Show that if A-1 exists, then f eAT dr = A-(eAt – I) = (e4t – I)A-1.

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Q: If iz'+z?-z+i=0, then show that z=1. 3

A: Given z3 + z2 -z + i =0 We have to show that z = 1 iz3 + z2 -z + i =0iz(z2+i) + (z2 + i) = 0(z2 + i)…

Q: Express the following as a linear combination of u = (2, 1, 3), v = (1, -1, 4) and w = (3, 2, 6).…

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Q: Give algebraic proofs of properties (1)u + (-u) = 0 ,(2) (c + d)u = cu+ du

A: Let be a vector such that  Multiply  with -1. Adding the two results,  Thus,is the additive…

Q: 2. Answer one of the following questions: (a) Show that a necessary and sufficient condition that…

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Q: 1. CHAIN OF REASONING: F= -E-R -S E → W RvS WV-S

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: - 7 Let v, = 1 6. V3 = -7 and u = 7 Determine if u is in Nul A, where A = V1 V2 V3 6 6 7 6 Is u in…

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Q: Which one of the following is always true?* fry fyx fry = fyy %3D %3D O Option 2 Option 4 fxx = fyy…

A: fxx, fyy depend on function and are equal in very rare cases.    While,  fxy and fyx are called…

Q: du = In (– u) + C If u<0, then u (A) True В False

A: The statement is  If u &lt; 0 then ∫duu=ln(-u)+C

Q: If I (F14)- s²+1 SO is given by? a) V(s? + 1)³

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Q: 6. Determine whether each of these statements is true or false. а) х€ {{x}, {x, у}, (x, у, 2}} b)…

A: State the true or false

Q: It gER[a,b] and if h(x)=q(x) except for a finite number of points in [ab],then prove that he R[ab]…

A: The continuous set of [a,b] should be divided into finite sets first.

Q: 2 2 22 if== prove that 22 a¯x +b¯y¯ +c¯=¯ 3, ,3, 3 a'x + b°y +c°z xyz abc %3D

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Q: Which of the following statements is always true (select all that apply)? Р (AUB) — P(A) + Р (В) Р…

A: The probability of an event is the chance of occurrence of that event.

Q: (P(A U B) is . . P(A) U P(B X

A: Two cases arise while finding the union of two sets. Case 1: If A and B are mutually exclusive sets,…

Q: 6. Evaluate u x v, where u = -e, - 2e, + 2e,, v = 2e, - 2e, +e,.

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Q: Let (pos S) be the set of all positive combinations of the points of S. Which of the following…

A: We need to find out which statements are correct. To do that, we shall independently analyze both…

Q: iken that I+2=1 xpressyin terms of xand z.

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: 3. Determine whether each of these statements is true or false. а) ОєФ b) Ø E {0} c) {0} c Ø d) ø c…

A: We know that ϕ is subset of every set. And a∈A if a is an element of A.

Q: Question 32 Which of the following statements are True? Select ALL that apply. O u. (v - w) =v.u-w.u…

A: Solution

Q: TRUE/FALSE If A = A−1, then A must be equal to either I or −I.

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Q: Which of the following are meaningful and which are not? Explain.(a) (u · v) × w(b) (u × v) · w

A: Consider the given: a)   u⋅v×w is not meaningful as u⋅v is scalar and cross product of vector and…

Q: Which of the following are meaningful and which are not? Explain.(a) (u · v) × w

A: We know that if u,v and w are vector quantity then u.v is scaler quantity So, cross product of…

Q: If W(-10, 4), X(-3, -1), and Y(-5, 11) classify AWXY by its sides. Show all work to justify your…

A: The given coordinates are

Q: af 10x +11ly and = 11x. Which of the following is the best definition of (x,)) = If %3D Əx

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Q: Which of the following is a possible y" + k'y = 0

A: Given that: y''+k2y=0

Q: Let C ~ Cauchy(0,1). Show that C² + C-2 =9 4C² + 2.

A: c^2+1/c^2 &gt;2 thats why it is equal to 4c^2+2

Q: 6) Given: <1 and <2 are not complementary Prove: <C is not a right angle A

A: As per our guidelines , we can not solve more than one question .Kindly repost the reamaining…

Q: Which of these statements is/are true? a)0 E Ø c){0} C Ø e){0} € {0} b)Ø e {0} d)Ø c {0} f){Ø} c {0}

A: The given question is related to set theory and logic. The solution is explained below.

Q: u + 4 du 7z u? +1 = (x)6 g'(x) : | HINT: u + 4 -du 5x u + 4 u + 4 -du -du + u? +1 u2 +1 u? + 1

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Q: Let -1 2 2 A = 1 -1 0 and U =|-2, then determine if %3D 3 -1 2 U is in Nul A. U is in Col A (i) (ii)

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Q: 2. Let A, B, and C be as in Exercise 1, let D = {3,2}, and let E = {2,3, 2}. Determine which of the…

A: See solution below. Properties of sets have been used.

Q: ) Prove that Вiт.m) - I(z)(m) for m >0 22'T(m +) 2

A: We use the property of Beta function and relation between Beta and Gamma function to prove the…

Q: Nhich of the following is true? * If A = (x: x [B| |A| < |B[ |A|

A: To solve the following problem, we use the defination of cardinality of a set. Cardinality of a Set…

Q: E==Iw2 + U, for I 2.

A: Given:              E=12I W2+U           E-U=12I W2   Multiplying 2 on both sides        2E-U=2×12I…

Q: a- If A = -1 %3D 2 and B = -41 prove that (A + B)T = AT + B". 12 [1/2 - If A-1 =1/2 -1/2) and |A| =…

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Q: (2) Let (x)S Hg(x)S Hc(x). Prove that AN(BỤC)=(ANB)U(ANC).

A: 2. To prove the above equality we need to show that A∩B∪C⊂A∩B∪A∩C andA∩B∪A∩C⊂A∩B∪C

Q: if H0 is u equal to 21, H1 is u is greater than 21, then the hypothesis is Oa Two tailed b. One…

A: Right tailed TEST:A right tailed test (sometimes called an upper test) is where your hypothesis…

Q: а. 2 ихх — иху — 4uy a2 u az u b. əx² azu ди +4 +34 + u = 0 дхду a?u = 2", k < 0 ax ду ди C. k ax?…

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Q: (mp + mp)V = (mẸ + mp)V¢cOS & = mf(V)F + mp(Viz)p = mgVg COs0 + mpVp (mp + mp)Vy = -(mp + mp)V¢sin o…

A: From the given equations we have,mF+mPvfx=mF+mPvfcos∅       ...........(1)mF+mPvfy=-mF+mPvfsin∅…

Q: Which of the following are always true, and which are not alwaystrue? Give reasons for your answers.…

A: To state whether the statement u×v·v=0 is true or false. Solution: Let u=a1i+b1j+c1k and…

Q: make v the subject 1/f=1/u+1/v

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Q: Then prove that 3 (i) P (AUB) > 1 (ii) <P (An B) S 10

A: Answer: From the given data, P(A) = 3/5 and P(B) = 1/2

Q: Express the following as a linear combination of u=(2, 1, 3), v= (1, -1, 4) and w=(2, 8, 8). (5, 14,…

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Q: 3. Let B = Consider T : R2,2 → R²,² defined by T(A) = AB – BA. Let [o o] Bị and B2 :

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