Prove the following statements (a, g is multilinear and alternating (b) If V=F", W=F₁ and T=LA for some A Man (F), then 9 = (det A/. f

Q: If f-(a, b) = 0 and fy(a, b) = 0, then Vf(a, b) = 0.

A: Given,           fxa,b=0   and   fya,b=0

Q: [T 2] 13) Did you know that the word "facetious" is the only word in the English language with all 5…

A: word= "facetious"

Q: Find |ATI, JA3I, |ATAI, and 19A|. -3 5 A = 7 1 (a) JATI (b) JA31 (c) JATAI (d) 19A|

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Q: [t +3 If A = -1 6. t- 3 -6 one of the following must be true? 1 t+ 4] A) The rank is 3 ift#-4, B)…

A: Rank of the Matrix, and it's properties

Q: Let A = 4a, + 2a, - a and B a and B = aa + Ba, +3a₂ (a) If A and B are parallel, find a and B (b) If…

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Q: Suppose Z∼N(0,1). Then P(2 ≤ Z ≤ 3) is the same as

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Q: 10) If 1+ abt = c where a, b, and c are positive, determine the value of t. %3D

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Q: If (f +g) € R[a, b] , then (f.9) € R(a, b] (f - 9) € R[a, b] E R[a, b] none of these

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Q: O show that 2. I| a+ V 1= 11 + 1i if and only if ū. ů =0 %3D

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Q: the Feurier tranefrn XC10) for the Pulse f the Sapual derlribed bekw: Frind 「-2, -ろs トヒへロ X(4) %3D…

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Q: 6. Let F = (-6, 5)U{-10, 10} U [7, 11). Find max F, min F, sup F, and inf F if they exist.

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Q: 2 let -27 Aslo -3 1470 -4 find AB+BA,AA"AA, (3A=2B)°C A'C..

A: "Since you have posted a question with multiple subparts, we will solve first three subparts for…

Q: COSZ 2) if Res(f,x) of the function f(2)=- a) -3/8 b) #-6 2ti c) 1/e d) 8/5 -is

A: To find Resf, π of the function fz=cos zz2 z-π3.

Q: • r : (x, Y, z) = (7, 8, 2) + X(-3, –8, 2) %3D 7 – x y – 8 - x y – 8 2 – z • S : -7 -6 4

A: Given query is to find the angle between two line.

Q: 6.- Evaluate T(au + bữ), considering the following 1 T(ī) = 2, T(5) = , T(ī) 2, a = -1 and b = 2 3…

A: T(au+bv)=T(au)+T(bv)

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: If w(f.9) = , then w(s.S+9) = (A) (B) - (C) 22 (D) -22 (E) None

A: Ans:- If w(f,g)=x2, then we have to find the value of w(f,f+g).

Q: 1) slz) = 3 -3 A) Yes B) No

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Hoist meihanism with a colera tion finu dis Plucement *こV1+o.256 ;PVニomis Sz3m for もこos and…

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Q: AN 3. Given R(x) = a) R (-1 3x-1 TED COMPILED ANDEDIB COMPILED AND EDITE COMPILED AND SoCOMPILED AND…

A: This is a composition of functions.

Q: End the cquation ot the perpeadicular to tie line KEy=4tat goes thousn the point (0,2).

A: topic - equation of perpendicular line

Q: What is the relations (5)/(8) and (8)/(10) Drag and drop a tern

A: Ok

Q: es (or+.1). COS Using P, (x), eshimate cas

A: In the question it is provided a function fi=cosπ+i The objective is to estimate the above function…

Q: D.4) show that is boundled) abng the if I sinz line&CXoy):dX-By =of Straight then

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Q: Suppose ū = (0, -3, –2) and ū = (-1, –4, –5). Then: u + v= u – v= v – u= 5u= 2u – 4ū=

A: Givenu¯ =0,-3,-2v¯ =-1,-4,-5

Q: If n(A) = 46, n(B) = 19, and n(AN B) 19, and n(An B) = 4, find n(A U B).

A:

Q: If w=f(p, q, r), where p-z2-y², q=y²-22, and r = 22-2², show that 1 Ow x 8x + 1 8w у ду + 18w z Əz…

A: Given w=f(p,q,r)and p=x2-y2,   q=y2-z2 and r=z2-x2

Q: 4. Which relation between x and u yields 16+x² = 4/1+u?

A: Given:

Q: If i = (1,0), then Difz(-3,4) = fry(-3, 4). O True False

A: If u→=1,0, then we have to check the given statement is true of false…

Q: 15) Find u x v for u = and v = .

A: Given vectors are, u = -7, 1, 12 = -7 i^ + j^ + 12 k^v = 2, 2, 3 = 2 i^ + 2 j^ + 2 k^

Q: ..***a***** . Let x (m, 1,0,-2)", m > 0 and ||x||2 = V30, then Select one: a. 6 b. 7 с. 5 d. 4

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Q: [1 3 0] If A = 1 2 1, then the Accompanying worker for Lo 1 4] 1. (a2,) | A. -4 В. -12 2. (a32) 3.…

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Q: Find the per pendicualar olistace from the P (5,6) to the line -2xr+3Y+4=0.

A: Formula for perpendicular distance is as below : Given :-2x+3y+4=0Ax+By+C=0A=-2B=3C=4 Point  (m , n…

Q: 4. (a) Given the digraph G = (V, E) below, list out V and E. V₁ JS Ju (b) Given the digraph G = (V,…

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Q: Let x = (m , 1 , 0 , -2)", m > 0 and ||x|l2 = v30, then m = Select one: а. 4 b. 5 с. 6 d. 7

A: