13. Write the reduced echelon form of a 3 x 3 matrix A such that the first two columns of A are pivot columns and 3 0 - [8] A -2 ham
13. Write the reduced echelon form of a 3 x 3 matrix A such that the first two columns of A are pivot columns and 3 0 - [8] A -2 ham
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
13
![hree
each
stem
ains
ving
m in
m.
blem
9. Write the vector
[5] as the sum of two vectors,
one on the line {(x, y): y = 2x} and one on the line
{(x, y): y = x/2}.
10. Let a₁, a2, and b be the vectors in R2 shown in the figure, and
let A = [a₁ a₂]. Does the equation Ax = b have a solution?
If so, is the solution unique? Explain.
a₂
11. Construct a 2 x 3 matrix A, not in echelon form, such that the
solution of Ax = 0 is a line R³.
12. Construct a 2 x 3 matrix A, not in echelon form, such that the
solution of Ax = 0 is a plane in R³.
A
13. Write the reduced echelon form of a 3 x 3 matrix A such
that the first two columns of A are pivot columns and
3
-2
]-[8]
x2
X1
14. Determine the value(s) of a such that
a.
linearly independent.
15. In (a) and (b), suppose the vectors are linearly independent.
f? Justify your
What can you say about the numbers a, ....
answers. [Hint: Use a theorem for (b).]
a
b
e
{[a] · [a + 2]} is
d
800-888
b.
10
a
4
B
2
WEB](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad941f7b-34e1-41bc-b27d-c60dbcd610a1%2F3a7fcf54-af1c-409d-b81b-c325e7971b5c%2Fnfuh34q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:hree
each
stem
ains
ving
m in
m.
blem
9. Write the vector
[5] as the sum of two vectors,
one on the line {(x, y): y = 2x} and one on the line
{(x, y): y = x/2}.
10. Let a₁, a2, and b be the vectors in R2 shown in the figure, and
let A = [a₁ a₂]. Does the equation Ax = b have a solution?
If so, is the solution unique? Explain.
a₂
11. Construct a 2 x 3 matrix A, not in echelon form, such that the
solution of Ax = 0 is a line R³.
12. Construct a 2 x 3 matrix A, not in echelon form, such that the
solution of Ax = 0 is a plane in R³.
A
13. Write the reduced echelon form of a 3 x 3 matrix A such
that the first two columns of A are pivot columns and
3
-2
]-[8]
x2
X1
14. Determine the value(s) of a such that
a.
linearly independent.
15. In (a) and (b), suppose the vectors are linearly independent.
f? Justify your
What can you say about the numbers a, ....
answers. [Hint: Use a theorem for (b).]
a
b
e
{[a] · [a + 2]} is
d
800-888
b.
10
a
4
B
2
WEB
Expert Solution
Step 1
13.
Given that .
We have to find a matrix that has first two columns of are pivot and satisfies the given condition.
Step by step
Solved in 3 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
