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- Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is {v1,v2,v3} linearly independent? Write all zeroes if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of v1, v2, and v3. a). Is {v1,v2} linearly independent? Write all zeroes if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of v1 and v2. c). Write the dimension of span {v1,v2,v3}Determine whether the set {p1,p2,p3} is linearly independent in P2, where p1 = 2+x+3x^2 +4x^3, p2 = 4+3x+2x^2 +x^3 and p3 = 1+2x+3x^2 +4x^3. Show all working
- 3) S contains only the vectors (-2+x-x² - 2x³), (4 + x - x² + 2x³), (8 + 5x -5x²+2x³), (10 + 7x - 7x² + 2x³). The new linearly independent set with the same span would beIf there are no vectors in the set S = {a1; a2; a3} from R^3 who is a multipleof one of the other vectors. Is the set S linearly independent or linearly dependent?Express the vector (-1,5, -6) in Ras a linear combination of (2,0,7), (2,4,5) and (2,-12,13).
- Let S = {v1, v2, v3} be a set of linearly independent vectors in R^3. (a) Are the vectors in the set T1 = {v1, v1 + v3, v3} linearly independent? Show how you arrived at your answer. (b) Are the vectors in the set T2 = {v1 − v3, 3v1 + v2, v2 + 5v3} linearly independent? Show how you arrived at your answer.Determine whether or not →v = (3, 9, −4, −2) ∈ R^4 is a linear combination of →u1 = (1, −2, 0, 3), →u2 = (2, 3, 0,−1), and →u3 = (2, −1, 2, 1), i.e., whether or not →v ∈ span (→u1, →u2, →u3).Suppose A is a 2x2 invertible Martix. Is the following statement true or false? For each vector b, which is an element of R^2, there is one and only one vector x, which in an element of R^2, such that A*vector x=vector b.
- Find the vector that has the same direction as <6, 3, −2> but has length 2.Show that the vectors are linearly dependent or linearly independent. note: {2t^2 − 1, t + 1},P2:The space of all polynomials with a degree less than 2 and 2Show that the vectors X1 = 5e3t and (3)-* 2et X2 = Tet form a linearly independent set.
