v₁ (2,1,3,4) 2₂ (-4,2,3,1)=(2,9, 21, 22)
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- Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if anything, can weconclude about the possible values of |xTy|?For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?8. Check whether (1, 2), (2, 3), (6, 0) are linearly independent or not?
- 5) Find the initial point of the vector that is equivalent to u = (1, 1, 3) and whose terminal point is B(−1, −1, 2).Show that a set of vectors, which contains a set of linearly dependent vectors, is linearly dependent. What is the analogous statement about linearly independent vectors?Under what conditions on the sacalr 'a' are the vectors (a,1,0),(1,a,1) and (0,1,a) in R\power{3} linearly dependent?
- Determine (if they exist) the values of the parameters α and β so that the vector (4, 9, -57, 17) can be written as a linear combination of (2,−1,−1,3) and (1,−1,2,1), so that (4,9,−57,17)=α(2,−1,−1,3)+β(1,−1,2,1)Let a = (2,3,6) and b = (3,4,2) be vectors. Compute the cross product aXbWhen the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . , un, v} is linearly dependent, prove that v is a linear combination of the ui’s.
- Are the vectors (-3,0,4), (5,-1,2), and (1,1,3) linearly independent in R3?Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W contains n + 1 distinct vectors, W is linearly dependent.In Exercises 1–5, find the length and direction (when defined) of u * v and v * u. 1. u = 2i - 2j - k, v = i - k 2. u = 2i + 3j, v =-i + j 3. u = 2i - 2j + 4k, v =-i + j - 2k 4. u = i + j - k, v = 0 5. u = 2i, v =-3j