For the matrix the set is the column space of A. The vector v = has [select all that apply] ✔a unique solution ✔ infinitely many solutions Ono solution. S = {b € R³ : b = Ax_ for some x¤R³} A = In this case the column space of A is x 3 -3 1 (CEA) 4 -2 3 -18 12 -11 Y Z belongs to this set whenever the augmented matrix 3 -3 1 x 4 -2 3 Y -18 12 -11z, By row reducing, we find that saying v ES is equivalent to x, y and z satisfying a linear condition of the form ax+by+cz = 0. Specifically, this condition is equivalent to x/45+y/30+z/9=0 a plane through the origin
For the matrix the set is the column space of A. The vector v = has [select all that apply] ✔a unique solution ✔ infinitely many solutions Ono solution. S = {b € R³ : b = Ax_ for some x¤R³} A = In this case the column space of A is x 3 -3 1 (CEA) 4 -2 3 -18 12 -11 Y Z belongs to this set whenever the augmented matrix 3 -3 1 x 4 -2 3 Y -18 12 -11z, By row reducing, we find that saying v ES is equivalent to x, y and z satisfying a linear condition of the form ax+by+cz = 0. Specifically, this condition is equivalent to x/45+y/30+z/9=0 a plane through the origin
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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![For the matrix
the set
is the column space of A. The vector v =
has [select all that apply]
✔a unique solution
✔ infinitely many solutions
Ono solution.
S = {b € R³ : b = Ax_ for some x¤R³}
A =
In this case the column space of A is
x
3
-3 1
(CEA)
4 -2 3
-18
12 -11
Y
Z
belongs to this set whenever the augmented matrix
3 -3 1 x
4 -2 3
Y
-18 12
-11z,
By row reducing, we find that saying v ES is equivalent to x, y and z satisfying a linear condition of the form
ax+by+cz = 0. Specifically, this condition is equivalent to
x/45+y/30+z/9=0
a plane through the origin](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15dc8ad5-c38d-4e49-b457-90ead50d7ae7%2F0a0228d6-281e-4a9f-bcb1-2aac2d5e23e2%2Fip6f68k_processed.png&w=3840&q=75)
Transcribed Image Text:For the matrix
the set
is the column space of A. The vector v =
has [select all that apply]
✔a unique solution
✔ infinitely many solutions
Ono solution.
S = {b € R³ : b = Ax_ for some x¤R³}
A =
In this case the column space of A is
x
3
-3 1
(CEA)
4 -2 3
-18
12 -11
Y
Z
belongs to this set whenever the augmented matrix
3 -3 1 x
4 -2 3
Y
-18 12
-11z,
By row reducing, we find that saying v ES is equivalent to x, y and z satisfying a linear condition of the form
ax+by+cz = 0. Specifically, this condition is equivalent to
x/45+y/30+z/9=0
a plane through the origin
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