In each part express the vector as a linear combination of ~p1 = 2 + x + 4x 2, ~p2 = 1 - x + 3x 2, and ~p3 = 3 + 2x + 5x 2. i. -97x15x 2 ii. 6 + 11x + 6x 2 iii. O iv. 7 + 8x + 9x 2

Q: Find the parametric vector form for the solution of the system, where all coefficient one in X₁ +…

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Q: Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is…

A: Solution: (a) We see,            v1 + v2 = [0 5 8] + [12 -20 5]                          = [0+12…

Q: Express the following system of linear equations as a vector equation. 1x1 +4x2 - 6x3 = -5 -2x1 +…

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Q: Find a non-zero vector that is orthogonal to (-7,6,5).   Separate your entries by commas, and…

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Q: 5. i ',, Find the solution space and write it as a linear combination of vectors. - x3 + 5x4 X2 +…

A: Given that x1-x3+5x4=0 x2+4x3-3x4=0

Q: 7. (а) X1 3x2 = 1 2x1 - 6х, — 2 | %3D

A: The solution is given as

Q: please help thank you so much

A: Ans 24:

Q: 3. Write u= -=[3] as a sum of vectors, one in the direction of and another orthoganal to a. -1 a=

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Q: Suppose the equation ax + by = c corresponds to the vector (a, b, c). To what equation will…

A: Given that:The equation ax+by=c corresponds to the vector ⟨a,b,c⟩. (1).The given vector is:…

Q: There are four vectors (1,2,3), (1,-1,2), (2,4,6) and (2,6,c). If there is a condition in which the…

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Q: Calculate the area of the parallelogram determined by the points (-1 , -1), (2 , 4), (4 , 3) and (7…

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Q: Suppose the polynomial ax² + bx + c corresponds to the vector (a, b, c). 2 To what polynomial will…

A: ConclusionIn the context of the given problem, where vectors correspond to the coefficients of a…

Q: If the cross product of two nonzero vectors is the zero vector, then each of the two vectors is a…

A: Explanation of the answer is as follows

Q: Write a system of equations that is equivalent to the given vector equation. -2 X1 - 2 4 + 8. X2 +…

A: The given vector equation is                                   x1  4-2+x285+x3-2   1=00 We have to…

Q: what if it was the same vector, but 5y^2j?

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Q: Use a grid and draw arrows to represent the following vectors. You canchoose any starting point you…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…