1. Consider the matrix [1 0 0 1 1 1] 1 10 21 3 A = 2 1 1 2 1 3 and the vector b [10 0 1 1 1 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. Consider the matrix [1 0 0 1 1 1] 1 10 21 3 A = 2 1 1 2 1 3 and the vector b [10 0 1 1 1 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.
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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please solve all parts
![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%2Fbcea9bf3-f03b-4160-9305-0aa85d132f0b%2F473ee716-3241-45a7-a04c-2429183f075b%2Fur9sk8p_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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