Do not solve just prove using grade 12 knowloge No matrix  3. Show that the planes below form a triangular prism. Determine a direction vector with integer components for the line of intersection for each pair o f planes : x + y – z + 2 = 0 2 x + 2 y – z – 6 = 0 4 x + 4 y – z + 5 = 0

Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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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: Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}.…

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Q: Find a vector a that has the same direction as (-8, 5, 8) but has length 3. Answer: a =

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Q: The graph below shows vectors u, v and w. 5- -5 -4 -3 ν 4 3 2 -2 2 3 -1 W -2 -3 -4 -5 Clear All…

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A: (.) Given vectors are,  (.) Linear combination: A vector  can be written as a linear combination of…

Q: Suppose the row echelon form of a system of equations is x−2y−9z == −10 y+2z == −1 Enter the…

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Q: Express the vector x as a linear combination of the u's. -17 U₁ = 0, U₂ = 5, U3 = 6, X = -43 -14…

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Q: Let u = (1, 2, 3), v = (2, 2, -1), and w = (4, 0, -4). Find 2u + 3v - w. STEP 1: Multiply each…

A: Given that the vectors u=1,2,3v=2,2,-1w=4,0,-4    .

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A: Given vectors a=(3, 4) and b=(4, 1)

Q: Compute for the cross product of the following pairs of vectors (-4, 3, 0) and (6, 2, -5). Then,…

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Q: Are the vectors ū = [4 -5 4], v = [2 2 -3] and w = [-1 -5 2] linearly independent? Choose If they…

A: To find Whether the given vectors are limearly independent or not.

Q: Express the vector v =-1 as a linear combination of the vectors -3 0,v2 4 and v3 -4 , if possible.…

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