In Exercises 1–6, determine which sets of
6.
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- 6. Show that the vectors (1,1,0), (1, 0, 1), and (0, 1, 1) generate F³.arrow_forward2. Write 3 as a linear combination of the vectors +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_forward
- 6. -2 Write -7 as a linear combination of the vectors 4 -1 一日一日一日 6. -2 -7 2 4arrow_forward98. Determine whether the vectors AB and PO are where A(1, 4, 1), B(−2, 2, 0), equivalent, P(2, 5, 7), and Q(−3, 2, 1).arrow_forwardIn Exercises 11–14, find the value(s) of h for which the vectors are linearly dependent. Justify each answer.arrow_forward
- 1. Find the sum of the vectors (3,-1) and (-1,5) and illustrate geometrically.arrow_forwardThe following question is from linear algebra first year: Factors the vector (6, -5, -1)t into three components a,b,c that satisfy the following conditions: a depends on (2,0,1)t, b depends on (1,2, 0)t and c is orthogonal to a and b. Please show it step by step. Can we get integers as answers?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_forward
- se. Justify_your answer 1 1 1 1 -1 is a linear combination of the vectors y,= 2 -1 V3= Show whether or not the vector V = ,V2= -1 -2 1 -1 Attach File Browse Mv Computerarrow_forward4. Give an example of vectors in R3 that spans R3. (show works)arrow_forward11) (Section 9.5,9.6) Find a unit vector that is orthongonal to both u and v . u3(2,-1,3) v=(1, 0, –2) 0.2.00 v=(1,0,-2) %3Darrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage