Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4v, + 5v2), v = (3, –4, –1), w = (1, 17) (a) the image of v (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.)

Q: skip the first 3 thank you

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Q: The plane passing through the three points A(4, –3, –4), B(-4, –3,2) and C(-3,3, –2) can be…

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Q: (а) (4, — 1, 2), (-4, 10, 2) (Ъ) (—3,0, 4), (5, — 1, 2), (1, 1, 3) (c) (8, – 1, 3), (4,0, 1)

A: As per rules, we will solve first three subparts: a) Given vectors are   u=4,-1,2, v=-4,10,2. To…

Q: Do question two only

A: Step 1: Assign variablesFrom the givena=⟨4,6,9⟩b=⟨−6,−3,2⟩Let:xa = 4ya = 6za = 9xb = -6yb = -3zb = 2…

Q: Do question 12 only

A: The given in item #12 is:∫04π​​∫01​∫0x2​xcos(y) dz dx dy Consider the innermost…

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A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Let L₁ be the line passing through the points Q₁=(4, -2,-4) and Q₂=(3, 1, -7) and let L₂ be the line…

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Q: Point P₁ lies on the line {₁:[4,4,-3]+t[2,1,−1],tER, and point P2 lies on the line…

A: Solution : Given that the lines l1 : 4,4,-3+t2,1,-1l2 : -2,-7,2+s3,2,-3

Q: Find the projection of the vector a = (2, 5, 1) on the vector b = (1, 1, 3) O a. (10/11)(ax + 3ay +…

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Q: Sketch a graph of each vector. 11) b=(-2V2,-1) 12) RS where R= (-6, 1) S= (-8,-10)

A: Solution (11.)

Q: Which of the following is a direction vector for the line through A (3, –2) and B(1, 2)? Select one:…

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Q: e) a unit vector perpendicular to both i and i f) the volume of the parallelepiped formed by vectors…

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Q: The first problem is Question 4: vector is described. Express the vector in terms of i and j. A…

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Q: Which of the following sets of vectors are linearly independent? A. (4, 8,-5), (-9, -4, -6), (-13,…

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

Q: Determine whether the lines L1 and L2 given by the vector equations are parallel, perpendicular, or…

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Q: Do question 10 only

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Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Given : The given set is  S = {(2, -1, 3) , (5, 0, 4)}. To find : We have to write the following…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Distance = 4.41

Q: 3 Consider the vectors a= =(2³₁) and b =(p+¹). 2p 8 Find the possible values of p for which a and b…

A: we have to find p.

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: Given,S = { (2, -1, 3), (5, 0, 4) }To find:  the vector as a linear combination of the vectors in S.…

Q: a = (3, 2, 4), b = (-3, 3, 0), c = (0, 0, -2) %3D (a) Find a x (b x c). a x (b x c) = || %3D (b)…

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Q: Do question 9 only

A: Step 1: Compute the Gradient of 𝑓Given f(x,y)=x2ey,Compute the partial…

Q: 4. (a) Determine if the four points P¿(1,1, –2), P2(4, 0, –3), P3(1,–5,10), and P,(-7,2, 4) lie on…

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