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A: Step 1:As you ask question 1, I solved it but if you need other parts you can ask.
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- Find the coordinate vector of [3, -4, 7] relative to the ordered basis B= ([1, 0, 0], [0, 0, 1], [2, 4, 0]) of R^3. Justify your work.Compute the flux of the vector field (x³, (2*, – æy³), out of the rectangle with vertices (0,0), (3,0), (3,2), and (0,2) 6Find the coordinate vector of [4, -2, 1] relative to the ordered basis B= ([0, 1, 1], [2, 0, 0], [0, 3, 0]) of R^3.
- Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a matrix whose Nullspace is spanLet x(¹) (t) = -3t e 4e-3t, 0 x (²) (t) = [_5e-³]; x (³) (t) = -5e-3t, Are the vectors x(¹) (t), x(²) (t) and x(³) (t) linearly independent? choose ◆ If the vectors are independent, enter zero in every answer blank since those 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 -3t [8] = 0[*]+[-+* 0 [4e-3t -5e-3t -0[ + -5e-3t -35e-3t -5e-3t -35e-3t8. (a) Show that the vectors v1 = (1, 2, 3, 4), v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a linearly dependent set in R*. (b) Express each vector as a linear combination of the other two.
- Find the components of the vector whose initial point is (2, 2, 4) and terminal point at (0, 2, 0).2- We can write the vector x = (19,–1, -) in R³ as a linear combination of the vectors x1 = (4,2, –1), x2 = (1,5,–1) and x3 = (2,-2,3), and the scalars are A:a, = -,a, = -,a, =-2 -,a2 = 5, az C: az = 5, az = -2,az B: a, = = 2 1 2 A В CWhat is the component form of the vector with an initial point of (-2,5) and a terminal point of (7,-3)?