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For the planes described by
4(x+1)+y+10(z-2)=-18,
and-8(x-2)+2(y+1)+3z=10
Write the
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- 3. If a = 3x - 5ỹ and b = -2x +9y, write the vector 5a-86 in terms of x and ySuppose the polynomial ax² + bx + c corresponds to the vector (a, b, c). 2 To what polynomial will (3,4,2) correspond? 3x+4x+2 2 To what polynomial will (3, -3, -5) correspond? 3x²-3x-5 To what polynomial should (3, 4, 2) + (3, -3, -5) correspond? 6x+x-3 What should the corresponding vector be? (6,1,-3) vector components) 2 To what polynomial should 2(3,4,2) correspond? 6x²+8x+4 J What should the corresponding vector be? (6,8,4) Submit Question A Part 2 of 5 Part 3 of 5 (Use to enclose the ▼ Part 4 of 5 Part 5 of 5 Based on the preceding, is there any significance to the componentwise sum of two vectors?" Defend your conclusion..please answer
- Solve for the vector x in terms of the vectors a and b. (If needed, use BOLD vector form on calcPad Vector menu.) x + 4a - b = 4(x + a) - (2a - b) X =Find the requested vector in R² where A = (-3,6), B = (8, –-6) and C = (7,4). -2AB + 7CB : help (vectors)define (2a - b + 4c, 3a-c, 4b + c) as a linear combination of three nonzero vectors
- formulate this probblem. There are currently 3 machines in a factory: P1, P2, and P3. Assume that this rectilinear shaped factory is located on the first quadrant of the coordinate system and one corner is at the origin (point (0,0)). The coordinates of the existing machines are as follows: P1=(10,15), P2=(20,25) ve P3=(40,5) To meet the increasing demand and respond to changing customer demands, the company decided to grow and acquired two new machines: N1 and N2. When these two machines are put into operation, they will exchange materials with each other and with the other three machines. 400 units of material will be transported between the 2 two new machines in a week. Similarly, 400 units will be transported between N1 and P1, 0 between N1 and P2, and 500 units between N1 and P3. The transportation between N2 and P1, P2, and P3 are 200, 100, and 0, respectively. Materials are transported with an overhead crane. This crane can move linearly in x and y coordinates and can move…The zero vector 0 = (0, 0, 0) can be written a linear combination of the vectors v., v,, and v- because 0 = Ov, + 0v, + 0v3. This is called the trivia! solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v., v,, and v- If not possible, enter IMPOSSIBLE.) V1 = (1, 0, 1), V2 = (-1, 1, 2), V3 = (0, 1, 6)a. Write the vector (-4,-8, 6) as a linear combination of a₁ (1, -3, -2), a₂ = (-5,–2,5) and ẩ3 = (−1,2,3). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ + 5ả₂ + 6ẩ3, which would be entered as 4a1 + 5a2 + 6a3. (-4,-8, 6) = -3a1+a2+2a3 b. Represent the vector (-4,-8,6) in terms of the ordered basis = {(1, −3,−2), (-5, -2,5),(-1,2,3)}. Your answer should be a vector of the general form . [(-4,-8,6)] =
- Are the vectors 16 + 16x – 12x², – 12 – 12x – 12x? and 18 + 18x – 3x2 linearly independent? linearly independent If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer. 0 = (16 + 16x – 12x²)+ (-12 – 12x – 12x²)+ (18 + 18x – 3x?).A direction vector for a line is any vector that joins two points on that line. Find a 8. It is not certain that you and your classmates will get direction vector for 2x + 5y exactly the same answer. How should your answers be related, however?a. Write the vector (23, -12, -19) as a linear combination of a₁ = (3, -2, -1), a2 (2, -3, -1) and ã3 = (-2, -2, 4). Express your answer in terms of the == named vectors. Your answer should be in the form 4ã₁ + 5ã2 + 6a3, which would be entered as 4a1 + 5a2 + 6a3. (23,-12,-19) b. Represent the vector (23, -12, -19) in terms of the ordered basis B={(3,-2,-1), (2, -3, -1), (-2, -2, 4)}. Your answer should be a vector of the general form . [(23, 12, 19)] B =