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For problem 19-22, determine whether the given set of
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- For what values of c are the vectors t + 3 and 2t + c2 + 2 in P1 linearly independent?arrow_forward1. Find all solutions: 2. In what ways can 88-8 and be written x+y ==0 a as a linear combination of [] [] [4], and ² 3. Show that the vector 2 is NOT contained in the span of the following three vectors 6 4. For which b are the vectors -0.0 x+2y+z=5 2x+3y-z=3 independent?arrow_forwardExpress each of the following vectors in R² as linear combinations of the vectors [3] and [3] (a) (b) (c) (d) 7 13 H 5 5 12 22 = || = = + + + + + 5 r 3 rarrow_forward
- [3] 1. Show whether the vector w = |1 is in span2 [5] 2. Show whether the following polynomial vectors are linearly independent or dependent. P1 = 1+ x, P2 = 1+ 2x², P3 = 2x + 3x²arrow_forwardSuppose that you are in the garden supply business. Naturally, one of the things that you sell is fertilizer. You have three brands available: Vigoro, Parker's, and Bleyer's. The amount of nitrogen, phosphoric acid, and potash per 100 pounds for each brand is given by the nutrient vectors T(x) = 2 ---A 32 p= b= = 11 Parker's Bleyer's T-¹(y) = V= T-1 7 66 Vigoro Determine the linear transformation T: R³ R³ that takes a vector of brand amounts (in hundreds of pounds) as input and gives the nutrient vector as output. Then find a formula for T-1, and use it to determine the amount of Vigoro, Parker's, and Bleyer's required to produce 44 pounds of nitrogen, 200 pounds of phosphoric acid and 412 pounds of potash. 44 (1)- 412 X 11 2 23 yarrow_forwardIf k is a real number, then the vectors (1, k), (k, k+ 56) are linearly independent precisely when k # a, b, where a = , 6 = and a < b.arrow_forward
- Let -0-0-0-0 V2 = w= -5 = -2 = = If possible, express w as a linear combination of the vectors V₁, V2 and v3. Otherwise, enter DNE. For example, the answer w = 4v₁ + 5v2 + 603 would be entered 4v1 + 5v2 + 6v3.arrow_forwardFor each of the following lists of vectors in R³, determine whether or not the first vector can be expressed as a linear combination of the other two. (a) (-2, 0,3), (1, 3,0), (2, 4, -1) (b) (1,2,3), (-3, 2, 1), (2, -1, −1) (c) (3, 4, 1), (1, -2, 1), (−2, —1, 1)arrow_forwardGet ||X||∞ and ||X||2 for the following vectors:arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage