ch em ins ing in n. lem the wing n in lem solution of 12. Construct a 2 x 3 matrix A, not in echel solution of Ax = 0 is a plane in R³. 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 []-[8] A 14. Determine the value(s) of a such that 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).] LATE a 000-000 b. a. a A = 1 2 b 3 4 is -[:] [₂] - d 16. Use Theorem 7 in Section 1.7 to explain why the columns of the matrix A are linearly independent. 0 0 0 5 0 0 6 8 0 7 9 10 b d 17. Explain why a set {V1, V2, V3, V4} in R5 must be linearly independent when {V₁, V2, V3} is linearly independent and V4 is not in Span {V₁, V2, V3}. 18. Suppose (V₁, V2} is a linearly independent set in R". Show that (V₁, V₁ + V₂} is also linearly independent.
ch em ins ing in n. lem the wing n in lem solution of 12. Construct a 2 x 3 matrix A, not in echel solution of Ax = 0 is a plane in R³. 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 []-[8] A 14. Determine the value(s) of a such that 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).] LATE a 000-000 b. a. a A = 1 2 b 3 4 is -[:] [₂] - d 16. Use Theorem 7 in Section 1.7 to explain why the columns of the matrix A are linearly independent. 0 0 0 5 0 0 6 8 0 7 9 10 b d 17. Explain why a set {V1, V2, V3, V4} in R5 must be linearly independent when {V₁, V2, V3} is linearly independent and V4 is not in Span {V₁, V2, V3}. 18. Suppose (V₁, V2} is a linearly independent set in R". Show that (V₁, V₁ + V₂} is also linearly independent.
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
17
![ch
em
ins
ing
in
n.
lem
the
wing
n in
lem
solution of
12. Construct a 2 x 3 matrix A, not in echel
solution of Ax = 0 is a plane in R³.
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
[]-[8]
A
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
000-000
b.
a
A =
1
2
b
3
4
-[:] [-]-
d
0
5
6
7
16. Use Theorem 7 in Section 1.7 to explain why the columns of
the matrix A are linearly independent.
0 0
0
0
8 0
9
10
b
is
d
17. Explain why a set {V1, V2, V3, V4} in R5 must be linearly
independent when {V₁, V2, V3} is linearly independent and V4
is not in Span {V₁, V2, V3}.
18. Suppose (V₁, V2} is a linearly independent set in R". Show
that (V₁, V₁ + V₂} is also linearly independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad941f7b-34e1-41bc-b27d-c60dbcd610a1%2Faa58a1bd-cb01-4c5c-9311-b09b0f5d7fa9%2F3ywr4y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:ch
em
ins
ing
in
n.
lem
the
wing
n in
lem
solution of
12. Construct a 2 x 3 matrix A, not in echel
solution of Ax = 0 is a plane in R³.
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
[]-[8]
A
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
000-000
b.
a
A =
1
2
b
3
4
-[:] [-]-
d
0
5
6
7
16. Use Theorem 7 in Section 1.7 to explain why the columns of
the matrix A are linearly independent.
0 0
0
0
8 0
9
10
b
is
d
17. Explain why a set {V1, V2, V3, V4} in R5 must be linearly
independent when {V₁, V2, V3} is linearly independent and V4
is not in Span {V₁, V2, V3}.
18. Suppose (V₁, V2} is a linearly independent set in R". Show
that (V₁, V₁ + V₂} is also linearly independent.
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