Determine which pairs of
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- Are the vectors –2 – 8x + 4x2, – 4 – 12x – 20x? and -4 – 14x – 6x? linearly independent? choose 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 = (-2 – 8x + 4x?)+ (-4 — 12г — 20г?)+ (-4 — 14г — ба?).arrow_forwardSection 5-2 : Vector Arithmetic 1. Given ā = 31 -9j and b = -6i +j compute each of the following. (a) 105 (b) 14ã + 205 (c) 8b – 3 2. Find a unit vector that points in the same direction as a = (10,-3,8,-2). 3. Find a unit vector that points in the opposite direction as č = 2i +7j - 5k . 4. Find a vector that points in the opposite direction as ā = (-3,–14,2) with a magnitude of 32. 5. Determine if i = (1,0,-4) and w= (9,3,1) are parallel vectors.arrow_forward5. Vectorsarrow_forward
- 2. Write 3 as a linear combination of the vectors +arrow_forwardPart b L Let U₁ = 1 + x + 4x², U₂ = 2x + 5x², U3 = 2 + x + 7x². Determine whether these three vectors are linearly independent or not.arrow_forwardExpress the vectors in Exercises 9–12 in terms of their lengths and directions.arrow_forward
- What is the component form of the vector represented by 2a when a (-23)7arrow_forwardExpress the vectors in Exercises 9–10 in terms of their lengths and directions. 9. 22i + 22j 10. -i - jarrow_forwardSolve the following exercises, you will need to show all your work to receive full credit. Consider the matrix, 2 1 -2 2 3 -4 1 1 1 - Knowing that f(t) = (t – 1)²(t - 2) is the characteristic polynomial, do the following: 1. find a basis of eigenvectors; 2. Find P such that P- AP is a diagonal matrix D. Give Darrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage