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)} , wz = {–7,8, 1} , wz {(-6,9, 1)} 3 -2 1 0\ A = 1 6 2 1 and T : R* H→ R° such that matrix A is the -3 0 7 1 transformation matrix in relation to bases B and B' a) Find a formula and a basis for T(21.72, #3, #4) and use this formula to get T(2,2,0,0) b Find Im(T) and a basi for the Im(T).What is the dim(Im(T))

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

A:

Q: Two students are named to present their work from a class of 12 students: 5 from electrical…

A: Total = 12 students Electrical = 5 students Telecommunication = 4 students  Computer = 3 students

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

A:

Q: Suppose v=(2,-1) and w=(-3,4). Find 2v —> 3w

A: v = (2,-1) = 2i-j w = (-3,4) = -3i+4j

Q: b) x = 5 + 4t,y = – 3+ 5t, z = 6 – 4t O (x, y, z) = (4, 5, – 4) + t(5, – 3, 6) ai+ bj + ck = (4i +…

A: We have to find the correct option

Q: 11. If d || e, mZ6 = 9x - 4, and m28= 4x + 67, then a. m25 = 6 7 b. m27= 8 e

A: Supplementary and corresponding angles

Q: 4 as a linear combination of v,, V2, V3 when the coefficient of v3 is 1. 14 Write -4 Ov, + - (OV2+v3…

A:

Q: 9. If y = V-|x|, then D =

A: We can differentiating given function in the in particular domain.

Q: a. selected student is male or from the Computing Engineering  b. selected student is female given…

A: Given two attributes, gender and Programmes as follows Gender\Programmes Computing Engineering…

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

A:

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: 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: Express the following as a linear combination of u = (6, 1, 7), v = (1, -1, 4) and w = (1, 8, 7).…

A:

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

A:

Q: Of the high blood pressure patients in a particular clinic, 62% are treated with medication X, the…

A: Given that, P(x) =0.62 P(y) =1-0.62 =0.38 P(Fainting |x)=0.014 P(Fainting |y)=0.029

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 →               →       v = (x, y), || v || = 4, and →           w = (−2x, −2y), then →…

A:

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) 2(u + 3v), and (c) 2v − u. u = (−7, 0, 0, 0, 9), v = (2, −3, −2, 3, 3)

A: a). b).

Q: Express the following as a linear combination of u= (3, 1, 7), v = (1, -1, 7) and w = (6, 3, 6).…

A:

Q: What must be the value of y if u = (1/3, y, -1/2), v = (6, 1/8, 10), and u · v = -5/2. 3 1 4 O 2

A:

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

A: u = (1, 2, 3)3u = (3×1, 3×2 , 3×3)3u = (3, 6, 9)v = (2, 2, -1)w = (4,0,-4)

Q: Let X ∼ N ( 1 , 4 ) and Y ∼ N ( 2 , 9 )be independent and let W = X2 +2Y + 3. Then what is the mean…

A: Given, Therefore,

Q: 2) y"+2y'tey = &t, y(9)= 2, y(0)= 7 et, ylo)= &, /(0)=-7

A:

Q: og 1 randomly barks 10% of the time while Dog 2 earks 30% of the time when strang en pass by their…

A: Given: Probability of dog 1 bark = 0.40 Probability of dog 2 bark  = 0.30 Expected number of people…

Q: Two students are named to present their work from a class of 12 students: 5 from electrical…

A: Given:   Department Number of students Electrical 5 telecommunication 3 Computer 4 Total…

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

A:

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

A: Given :u=(1,2,3)v=(2,2,-1)w=(4,3,-4)

Q: b) Evaluate ſ, S s,(x² + y² + z²)dxdydz.

A: Integrate with respect to x and plug the limits.

Q: If v = (3, – 1, 1) and w = (-2, –2, –2) , what is v x w ?

A: Here two vectors v and w are given, we want to find the cross product or vector product of the given…

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: 1, Y2, · · , Y9 and it is believed that Y; ~ N(u, 16). Find P(|Y – µl < 2). ...

A:

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: (6) If w = f(u, v), where u = x + y and v = x – y, show that = 2 ди

A:

Q: 2t+9 dt (t2–14t+46) 2t + 9 2t + 9 dt (t – 7)2 – 3° J[(t – 7)2 – 3]² Option 2 Option 1 2t + 9 dt [(t…

A: Here, to rewrite the given integral: ∫2t+9(t2-14t+46)52dt...(1)

Q: 13. If T:(x, y)– (x – 1, y + 6), then T':(x, y) → (__, .

A: GivenT(x,y)=(x-1,y+6)To findT-1(x,y)

Q: p(x, y) 3/24 2/24 1/24 1 2/24 5/24 2/24 2 6/24 1/24 2/24 Е(X), Е(Y), H(X), н(Y, НХ Ү), аnd HIX, Y)

A: It is an important part of statistics. It is widely used. Since the question has multiple sub parts…

Q: Express w as a linear combination of u and v: ? = (4,1), ? = (−2, −1), ? = (2, −2)

A: Let w = (4,1) u = (-2,-1) v=(2,-2) we can write this as: u-21 + v2-2 = 41   -2u + 2v = 4 u - 2v = 1…

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

A:

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)

A:

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)

A:

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

A: u=1,2,3v=2,2,-1w=4,3,-42u+v-w+3z=0

Q: 4 - - 5 2 - Let V = and W = - 4 3 2 | Find V· W.

A: Dot product of two vectors

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

A:

Q: Express the following as a linear combination of u = (5, 1, 6), v = (1, -1, 5) and w = = (1, 5, 6).…

A: The given vectors are  u=(5,1,6)v=(1,-1,5)w=(1,5,6) We have to write the given vectors in linear…