Given B = v1 {(0, 1, 1, 1)}, v2 = {2, 1, – 1, –1}, v3 {(1,4, –1,2)} , v4{(6,9, 4, 2)} B' = wi {(0, 8, 8)}, w2 = {-7,8, 1} , w3 {(-6, 9, 1)} %3D 3 -2 1 0 A = | 1 6 2 1 and T : R4 → R such that matrix A is the -3 0 7 1 transformation matrix in relation to bases B and B' a)Check that sets B'is a basis of R' and set B' is a basis of R

Q: Show that: If |z| = 1, then: z' + 4z + 5 z2 + 5z + 6

A: Given: z=1 Then show that: z3+4z+5z2+5z+6≤5

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

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Q: GIVEN: Z, = 3ej(z/6) Z, = 2ej(#/4) FIND: 1.) Z, Z,

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Q: Find (a) ||u||, (b) ||v||, (c) u ∙ v, and (d) d(u, v).u = (−3, 2, −2), v = (1, 3, 5)

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Q: describes. A v 1.4 <r< 5 and 0 <0 < 2n ? v 2.4 <r<5 and a/2 < e< 3n/2 B ? v 3.0 <r<5 and 3/2 < 0< 2n…

A: According to figure shown below, answer all questions.

Q: Let u = (1, 2, 3), v = (4, 4, -2), and w = (6, 2, -5). Find z, where 2u + v – w + 3z = 0. Z =

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Q: For what values of c is ||c(1, 2, 3)|| = 1?

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Q: Find (a) u ∙ v, (b) v ∙ v, (c) ||u||2, (d) (u ∙ v)v, and (e) u ∙ (5v).u = (4, 0, −3, 5), v = (0, 2,…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: in class of N students where girls and boys and boys ratio is p:q savita ranked rth from the top. if…

A: Total number of students in class= N Ratio of girls to boys: p:q And it is given that Savita ranked…

Q: Find (a) u ∙ v, (b) v ∙ v, (c) ||u||2, (d) (u ∙ v)v, and (e) u ∙ (5v).u = (3, 4), v = (2, −3)

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: For u=⟨4,−2⟩ and v=⟨−5​,5⟩​,find u•v.

A:

Q: A friend who lives in Los Angeles makes frequent consultingtrips to Washington, D.C.; 50% of the…

A: Defining  A1: Travelling on the airplane #1A2: Travelling on the airplane #2A3: Travelling on the…

Q: (b) F= Ewxv(4, 5, 9, 13, 15) + d(0, 1, 7, 11, 12) w,x,y,z

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Q: Given w= (-3, 11), s=(-4, – 5), and r= s= (-4, - 5), and r= (4, 9), find 3r- (w+s). 3r-(w+s) = (|

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Q: Evaluate for r=(3,5) , s=(-6,4) , and t=(6,-1). 2r-(s+t)=

A: Recall the following facts.

Q: Find (a) u ∙ v, (b) v ∙ v, (c) ||u||2, (d) (u ∙ v)v, and (e) u ∙ (5v).u = (2, −2, 1), v = (2, −1,…

A: Given

Q: If W (2t – 1, y (t), 4t – 7) = -20, then y (t) = O f +5 O ² +3 O 2 - 5 O ² – 3

A: We will solve this by calculate  wronskian

Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (1, −2, −3), v = (3, 1, 0)

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Q: Find (a) u − v, (b) 2(u + 3v), and (c) 2v − u. u = (−7, 0, 0, 0, 9), v = (2, −3, −2, 3, 3)

A: a). b).

Q: Find w, x, y, and z so that W X 4 3 8 -3 2 4 -4 |

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Q: Express the following as linear combinations of 1= (2, 1, 4), v= (1, – 1, 3), and w= (3, 2, 5). 8.…

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Q: Find (a) ||u||, (b) ||v||, (c) u ∙ v, and (d) d(u, v).u = (1, 4), v = (2, 1)

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: Let u = (1, 2, 3), v = (4, 4, -2), and w = (6, -1, -2). Find z, where 2u + v – w + 3z = 0. z =

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

A: Let's consider w = (a, b, c, d) So w + u = (a, b, c, d) + (1, -1, 0, 1) = (a + 1, b - 1, c, d + 1)

Q: S(r, y) = S2, 0<r<y< 1, 10, elsewhere. Determine if X and Y are independent.

A: We have to check whether , X and Y are independent First we will find out the marginal probability…

Q: (d) The student prefers decaffeinated coffee, given that the student being selected from the male…

A: Given: data To find i) P(student prefer decaffeinated | student is male) ii) P(student is male |…

Q: Express the following as a linear combination of u = (4, 1, 6), v = (1, -1, 6) and w = (1, 6, 7).…

A: The objective is to find (7, 10,7) as linear combination of u, v, w.

Q: Find u · v, u· u, ||v||2, (u· v)v, and u · (3v). u = (4, -2, 5), v = = (0, 6, 3) (a) u V (b) (c)…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: If A 3 4a, — 2а, + ба, and B %3D 12aа, + 18а, — 8а, determine: (а) А — ЗВ (b) (2A + 5B)/в| (с) а, XА…

A: Given, A =4ax -2ay +6az B= 12ax +18ay -8az

Q: Find (a) u ∙ v, (b) v ∙ v, (c) ||u||2, (d) (u ∙ v)v, and (e) u ∙ (5v).u = (−1, 2), v = (2, −2)

A: u→=-1,2v→=2,-2a u→.v→=?     u→.v→=-12+2-2           =-2+-4          =-6u→.v→=-6

Q: What would be the linear equations for the functions, &amp; what would be the graphs?

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

Q: How is w = (-3, –13, 7) e R³ a linear combination of (0, -2, 2) and (1, 3, –1)? U = | V = O A. w =…

A: Given query is to find the correct option for linear combination.

Q: Let X=(1,0, – 1,- /2)'. Then, ||X||, = Select one: а. -V3 O . 2+V2 C. -V2

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Q: Find (a) u − v, (b) 2(u + 3v), and (c) 2v − u. u = (0, 4, 3, 4, 4), v = (6, 8, −3, 3, −5)

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Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (−1, 2, 1), v = (0, 1, 1)

A: Given  u = (-1,2,1) , v = (0,1,1)Find   (a) u+v      (b) 2v      (c) u-v      (d) 3u-2v

Q: If with n(F)=25, n(B)=12, n(T)=30, we have n(F∩T)=6, n(T∩B)=4, n(F∩B)=3, and there are 2 members who…

A: It is given that the number of members in team F ‘n(F)’ is 25.

Q: Show that: If |z| = 1, then: |z3 + 4z + 5 < 5 z + 5z + 6

A: Given: z=1 Then show that z3+4z+5z2+5z+6≤5

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (3, −2, 4), v = (1, 5, −3)

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Q: Let z = a?y – ry?, x = e 4, y = e2t, then which of the following is 2e2t + 2e 2t a. O b. -2e2t – 2e…

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Q: (E,E2 – k)z(k, l) = 0, - (E1 – kE,')z(k, l) = 0. -

A: The given operator form is: E1E2-kzk,l=0             (1)

Q: Q2 that : [(A+B), (C+ D)]=[A , C]+[A,D]+[B, C] + [B,D] 2- Find : [p,x].

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Q: 21 Let vi = 4 V2 = -7,V3 3 6 Does (V1, V2, V3) Sspan R?

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Q: Find fx(x,y,z), fy(x,y,z), f₂(x,y,z), and fyx (x,y,z) for the following. 3 f(x,y,z) = 4x³ + 2xy -…

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (3, −3, −3), v = (3, −3, 3)

A: Given: u=(3, −3, −3), v=(3, −3, 3)

Q: Let u = (1, 2, 3), v = (2, 2, –1), and w = (4, 3, -4). Find z, where 2u + v – w + 3z = 0. Z =

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Q: Given R = Z₁₂, M = {0, 4,8], then R/M is

A: We know the definition of quotient ring ,  R/M = a + M / a ∈ R We have given that , R = ℤ12  and  M…

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

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Q: 1. Suppose that u = (2, 7), v = (0, –1), and w = (-4, 6). (a) Find 2ū. (b) Find ū – w. (c) Find 3w +…

A: Given: ⃗u = (2,7), ⃗v = (0, -1), and ⃗w = (-4, 6) ⃗u = 2î+7ĵ , ⃗v = 0î-1ĵ , ⃗w = -4î+6ĵ (a).…

Q: Im e Z, Vn E Z,m = n + 5 Vn E Z, 3 X C N, \X| = n

A: on solving these statements with the help of an example we will get