4] Show that the following sets of vectors are linearlydependent in R3.(c) {{5, 2, -3), (3, 0, 4), (-3, 0, -4)}(d) {{1, 1, 1), (2, 2, 2), (0, 1, 5)}

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Answered: 4] Show that the following sets of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The following independent in R³ | = (1,2,3) ✓= (-1,0,-2) w = (1,4,4) True False vectors are linearly
Let v1= 2, 5 , 3 ) , v, = ( 1 , 1 , 1 ) and va = (4, -2 , 0 ) are vectors in R³ then are .a Linear dependent .b Linear independent
7) Find all vectors v in F such that 2v + (C) = (5)
Construct an orthonormal set of vectors in ℝ3 from the set of linearly independent vectors ? = {(1,1,1), (1,2,3), (2, −1,1)}.
The set of vectors {(1,1,0,0),(0,-1,0,0),(0,0,1,1),(1,0,1,1)} is linearly dependent. What is a valid expression of the last vector as a linear combination of the others? a. (1,0,1,1)=(1,1,0,0)+(0,-1,0,0)-(0,0,1,1) b. (1,0,1,1)=(1,1,0,0)+(0,-1,0,0)+(0,0,1,1) c. (1,0,1,1)=-(1,1,0,0)+(0,-1,0,0)+(0,0,1,1) d. (1,0,1,1)=2(1,1,0,0)+2(0,-1,0,0)+2(0,0,1,1)
2. If a set of vectors contains at least 2 vectors that are scalar multiples of each other, then the set is linearly dependent.
Express each of the following vectors in R² as linear combinations of the vectors [4] and (a) (b) (c) (d) 16 11 -36 17 -12 15 -20 = || = || - 4 Y + Y + -4 + Y + + + + A 4 -
Suppose v1, v2, v3, 04, Ū5 and ve are vectors in R6 satisfying the following linear relation: 201 + 302 – Ủ4 + 205 - Which of the following must be true? (Select all that apply) span(v1, v2, v3, 4, 06) = span(71, v3, 74, 05, V6) span(v1, v2, v3, 74, 05) = span(v1, v2, v4, V5, 76) span(v1, v2, v3, v4, v6) = span(v1, 02, v3, v4, Ü5 , v6) span(v1, v2, V3, v6)= span(73, v4, V5 , V6) O span(v1, v2, v3, V4, 05) = span(72, 03, v4, 05, V6 )
1- Determine whether the following sets of vectors are linearly dependent or linearly independent. a) (-3,0,4), (5,-1,2), (1,1,3) in R³ b) (1,0,0), (2,2,0), (3,3,3) in R³ 2- Verify that the set of vectors (-0.6, 0.8, 0), (0.8, 0.6, 0), (0, 0, 1) form an orthonormal basis for R³, then obtain an orthonormal basis from them. Express (3,7,-4) as a linear combination of the orthonormal basis. 3- Determine whether the following sets of vectors are linearly dependent or linearly independent. a) (1,1,0), (0,0,1), (0,1,1) in R³ b) (1,0,0), (2,2,0), (3,3,3) in R³ 4- Verify that the set of vectors (-0.6, 0.8, 0), (0.8, 0.6, 0), (0, 0, 1) form an orthogonal basis for R³, then obtain an orthonormal basis from them. Express (2,3,-4) as a linear combination of the orthonormal basis. 5- Find the coordinates of the vector u = (0,25, 1) with respect to the orthogonal basis v₁ = ( 3,4,0), V₂ = (−4, 3, 0 ) and v₂ = (−4,3,0) 6- Find the coordinates of the vector U = (7,5,2) with respect to the basis V₁ =…

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4] Show that the following sets of vectors are linearly dependent in R3. (c) {{5, 2, -3), (3, 0, 4), (-3, 0, -4)} (d) {{1, 1, 1), (2, 2, 2), (0, 1, 5)}