Anser the following with complete solution Let S = {v,,v2, v, } where v, =3a. Explain why the set S is not a basis for R?b. Find the dimension of the span of the set S.c. Find the basis B for R that contains the vectors v and v2Let M,, ·M2M, =%3Da.Show that the matrices are linearly independent.3b. Find the unique scalars c,,c,,c, such that the matrix M =can be written asM = c,M, +c,M, +c;M30 3Show that the matrix M =cannot be written as a linear combination of M,M,andM,-C.

1 4 Let S = {v,,v2,v,} where v, = -3 -7 %3D V2 = V3 1 1 3 1 3 a. Explain why the set S is not a basis for R ? b. Find the dimension of the span of the set S. c. Find the basis B for R that contains the vectors v and v2

1 4 Let S = {v,,v2,v,} where v, = -3 -7 %3D V2 = V3 1 1 3 1 3 a. Explain why the set S is not a basis for R ? b. Find the dimension of the span of the set S. c. Find the basis B for R that contains the vectors v and v2

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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Anser the following with complete solution

Let S = {v,,v2, v, } where v, =
3
a. Explain why the set S is not a basis for R?
b. Find the dimension of the span of the set S.
c. Find the basis B for R that contains the vectors v and v2
Let M,
, ·M2
M, =
%3D
a.
Show that the matrices are linearly independent.
3
b. Find the unique scalars c,,c,,c, such that the matrix M =
can be written as
M = c,M, +c,M, +c;M3
0 3
Show that the matrix M =
cannot be written as a linear combination of M,M,andM,-
C.

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