33. Suppose A is a 4 x 3 matrix and b is a vector in R4 with the property that Ax = b has a unique solution. What can you say about the reduced echelon form of A? Justify your answer.
33. Suppose A is a 4 x 3 matrix and b is a vector in R4 with the property that Ax = b has a unique solution. What can you say about the reduced echelon form of A? Justify your answer.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
33
![FI
in
act
hat
nd
tion
X2,
on as
se.
polic
r the
mbol
argument to the case of an arbitrary A with more rows than
columns.
32. Could a set of three vectors in R4 span all of R4? Explain.
What about n vectors in Rm when n is less than m?
33. Suppose A is a 4 x 3 matrix and b is a vector in R4 with the
property that Ax = b has a unique solution. What can you say
about the reduced echelon form of A? Justify your answer.
34. Suppose A is a 3 x 3 matrix and b is a vector in R³ with the
property that Ax = b has a unique solution. Explain why the
columns of A must span R³.
some
35. Let A be a 3 x 4 matrix, let y, and y2 be vectors in R³, and
let w = y₁ + y₂. Suppose y₁ = Ax₁ and y₂ = Ax2 for son
vectors X₁ and x₂ in R4. What fact allows you to conclude that
the system Ax = w is consistent? (Note: x₁ and x2 denote
vectors, not scalar entries in vectors.)
36. Let A be a 5 x 3 matrix, let y be a vector in R³, and let z
be a vector in R5. Suppose Ay = z. What fact allows you to
conclude that the system Ax = 4z is consistent?
[M] In Exercises 37-40, determine if the columns of the matrix
span R4
37.
39.
7
65 bań
2 -5
-6
4
-3
12 -7
4
11
-6
11
8
4 -9
7
15
10 -2
9 2
38.
11 -9
-8 7
-7 3 -9
10 -5 12
من نقاط
-3
5
-7 -4
6
-8
-7
4
-4
-9 -9
-9 11 16
97
5
مطار
7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdedb6468-f819-4716-87b0-c3be3de65b26%2F5cf14281-2cd5-4675-9acd-3622e83bb1fb%2Fguizt4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:FI
in
act
hat
nd
tion
X2,
on as
se.
polic
r the
mbol
argument to the case of an arbitrary A with more rows than
columns.
32. Could a set of three vectors in R4 span all of R4? Explain.
What about n vectors in Rm when n is less than m?
33. Suppose A is a 4 x 3 matrix and b is a vector in R4 with the
property that Ax = b has a unique solution. What can you say
about the reduced echelon form of A? Justify your answer.
34. Suppose A is a 3 x 3 matrix and b is a vector in R³ with the
property that Ax = b has a unique solution. Explain why the
columns of A must span R³.
some
35. Let A be a 3 x 4 matrix, let y, and y2 be vectors in R³, and
let w = y₁ + y₂. Suppose y₁ = Ax₁ and y₂ = Ax2 for son
vectors X₁ and x₂ in R4. What fact allows you to conclude that
the system Ax = w is consistent? (Note: x₁ and x2 denote
vectors, not scalar entries in vectors.)
36. Let A be a 5 x 3 matrix, let y be a vector in R³, and let z
be a vector in R5. Suppose Ay = z. What fact allows you to
conclude that the system Ax = 4z is consistent?
[M] In Exercises 37-40, determine if the columns of the matrix
span R4
37.
39.
7
65 bań
2 -5
-6
4
-3
12 -7
4
11
-6
11
8
4 -9
7
15
10 -2
9 2
38.
11 -9
-8 7
-7 3 -9
10 -5 12
من نقاط
-3
5
-7 -4
6
-8
-7
4
-4
-9 -9
-9 11 16
97
5
مطار
7
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