42. (а)Do the vectors vị =V2 =-1V3 =-1form a basis for R³?1, V3 =3form a basis(b)Do the vectors vịV4 =4V28.for R4?(c)For which value(s) of the constant c is the list of vectors vị =V2 =V3 =a basis of R3?||

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Answered: 3 2. (а) Do the vectors vị = -1 -1 form…

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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Make the vectors u1=(2,0,-1,1), u2=(1,1,-1,3), u3= (-1,1,1,-1) orthonormal.
6. Show that the vectors (1,1,0), (1, 0, 1), and (0, 1, 1) generate F³.
EXAMPLE 5 Vectors in R' Let u = (2, –4, 1) and v = ponents of the following vectors and draw them in R. (3, 0, – 1). Find the com- 1 b. -2v c. u + 2v а.
#1) Find the projection of U = ( 3 -5 ) onto V = ( 6, 2 ) . Then write U as the sum of two orthogonal vectors one which is projvU.#2) Find the projection of U = ( 3 4 ) onto V = ( 8, 2 ) . Then write U as the sum of two orthogonal vectors one which is projvU#3)Find the projection of U = ( 2 , 2 ) onto V = ( 6, 1 ) . Then write U as the sum of two orthogonal vectors one which is projvU2))#4)Find the projection of U = ( 4 , 2 ) onto V = ( 1 ,- 2 ) . Then write U as the sum of two orthogonal vectors one which is projvU3)
Let be the vector with initial point (8, 1) and terminal point (6,5). Express as a linear combination of the standard unit vectors. Ov=4i-2j 05-21-47 Ov=2i+4j Ov=-21-4j Ov=-2+47 O None of the above.

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3 2. (а) Do the vectors vị = -1 -1 form a basis for R³? , V3 = 1 > V2 = -I--- (b) Do the vectors vị = V2 = V3 = V4 = 4 form a basis for R4? (c) For which value(s) of the constant c is the list of vectors vị = V2 = C V3 = a basis of R3? C -1