1(d) Express each of vs,V6 as linear combinations of the vectors in (c). (e) Find the general solution to the linear system Ax = b, expressing your answer in the form of a vector plus a subspace. (f) Find a vector e such that Ax = c has no solution.
1(d) Express each of vs,V6 as linear combinations of the vectors in (c). (e) Find the general solution to the linear system Ax = b, expressing your answer in the form of a vector plus a subspace. (f) Find a vector e such that Ax = c has no solution.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
please solve (d), (e) (f)
![1. Consider the matrix
[1 0 0 1 1 1]
1 1 0 2 1 3
2 1 1 2 1 3
[1 0 0 1 1 1]
and the vector b
Let v1,... V6 be the vectors given by columns 1, ...,6 of A.
(a) Construct the augmented matrix [A|b] and use elementary row operations to reduce it to
reduced echelon form. Show each step.
(This row reduction can be used in almost everything that follows.)
(b) Find a basis for the null space of A. (Hint: solve Ax = 0.)
(c) Find a basis for the column space of A.
1(d) Express each of vs,V6 as linear combinations of the vectors in (c).
(e) Find the general solution to the linear system Ax = b, expressing your answer in the form of
a vector plus a subspace.
(f) Find a vector c such that Ax = c has no solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8a598c1-6b6b-41c6-8105-0a694dbd02da%2F4bd09327-f17a-497c-8ea2-374872b8bf1d%2F3ouzppf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider the matrix
[1 0 0 1 1 1]
1 1 0 2 1 3
2 1 1 2 1 3
[1 0 0 1 1 1]
and the vector b
Let v1,... V6 be the vectors given by columns 1, ...,6 of A.
(a) Construct the augmented matrix [A|b] and use elementary row operations to reduce it to
reduced echelon form. Show each step.
(This row reduction can be used in almost everything that follows.)
(b) Find a basis for the null space of A. (Hint: solve Ax = 0.)
(c) Find a basis for the column space of A.
1(d) Express each of vs,V6 as linear combinations of the vectors in (c).
(e) Find the general solution to the linear system Ax = b, expressing your answer in the form of
a vector plus a subspace.
(f) Find a vector c such that Ax = c has no solution.
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