2. Determine whether the following vectors are linearly dependent in R³: (O)--- ()--C) 1 , = , ez = 0 0 0 1 (a) e₁ = 0 2 ·()· · - () -- () --- () -- () 2 , V = W = (c) u = V= 2 1 1 1 -2 (b) u = (d) u = (-)--(-)--() 2 V= W = 0 6 -3 6
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- Find the vector equation of a line L going through the point P = (-5, -6) and parallel to the line generated by multiples of the vector v = --HA 1 L(t) - +t2. (a) (b) (c) Determine if the vectors are linearly independent. Justify your answer. [B] HI 22 and and " and ان ان -3 3How do I show that the vectors (1, 2), (0, 1), (-3, 4) are not linearly independent?
- For which real values of A do the following vectors form a linearly dependent set in R³? V₁ = 1₂ V2= V3 X₁ = 1 3' 3 1 (-₁^,-) = 1 3 2 3 - 1/3,^) A₂ =Q1. If the components of a contravariant vector in (x') coordinate system are (3,4). Find its components in (x') coordinate system, where x = 7x-5x? x2 = -5x' + 4x2Write the equation of the line passing through P with normal vector n in normal form and general form. - [⁹] 8·(0-8). P = (0, 0), n = (a) normal form (b) general form 0
- Let 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-3ta) Find F‘(0) for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find 3a +2b Note: an arrow representing direction should be on the alphabetsQ1. If the components of a contravariant vector in (x') coordinate system are (3,4). Find its components in (x') coordinate system, where x' = 7x' – 5x? x2 = -5x1 + 4x?