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Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 21CM

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9.
{(1,5), (-2,3)} is a spanning set for R². Express the vector (4, -3) as a linear
combination of the vectors in the spanning set.

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Find the vector v in the plane represented by the directed line segment from (4,-3) to (-2,6)
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}
Express the vector (-1,5, -6) in Ras a linear combination of (2,0,7), (2,4,5) and (2,-12,13).
Consider the vectors u1 = (1, 2, 1), u2 = (0, 3, 2) and u3 = (−2, 1, 1). Determine whether the set S = {u1, u2, u3} is a spanning set for R^3
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 be
Find the vector that has the same direction as <6, 3, −2> but has length 2.
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
If 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 R^3as a linear combination of (2,0,7),(2,4,5) and (2,-12,13).
make an example and prove it about five vectors spanning R⁴
11. a) By solving some equations with some unknowns, determine whether it is possible to write [5, -10, 1] as a linear combination of [4, -8, 4] and [-3, 6, 3], and if it is indeed possible, write the linear combination. 11b) Explain what your result in a) shows about the coplanarity of the 3 vectors.
Determine if the vectors < -2,-1,1>, <3,-4,-2> and <5,-10-8> are linearly independent.

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