Nicholas and Leonardo had been trying to solve a system of three equations in four unknowns, which they had written in matrix form as Ax = b. Nicholas reduced A to a row echelon form matrix U, but accidentally blurred out some of their work with blue cordial, leaving four of the entries unreadable. The row echelon form matrix now looks like (2 m n p U -0 0 6 q 0 0 0 0/ (a) Given only this information, solect all options that give a possiblo geometrical description of the solutions of the systom of aquations. O the empty set O a point a line a plane all of R (b) Leonardo remermbers that three specific solutions for the system are and Nicholas says. "That's great That means we can write a general solution to the system of equations in the form or perhaps as for some vectors a, v,, va c R' and real parameters t, and tg. Hmmmm, Im not sure which, maybe we need even more vectors and paramelers. Can you help me? Find a parametric vector form of the solution to the system of equations Ax = b given the three specific solutions above and enter it in the box below the syntax advice
Nicholas and Leonardo had been trying to solve a system of three equations in four unknowns, which they had written in matrix form as Ax = b. Nicholas reduced A to a row echelon form matrix U, but accidentally blurred out some of their work with blue cordial, leaving four of the entries unreadable. The row echelon form matrix now looks like (2 m n p U -0 0 6 q 0 0 0 0/ (a) Given only this information, solect all options that give a possiblo geometrical description of the solutions of the systom of aquations. O the empty set O a point a line a plane all of R (b) Leonardo remermbers that three specific solutions for the system are and Nicholas says. "That's great That means we can write a general solution to the system of equations in the form or perhaps as for some vectors a, v,, va c R' and real parameters t, and tg. Hmmmm, Im not sure which, maybe we need even more vectors and paramelers. Can you help me? Find a parametric vector form of the solution to the system of equations Ax = b given the three specific solutions above and enter it in the box below the syntax advice
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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Question
a,b please
![Nicholas and Leonardo had been trying to solve a system of three equations in four unknowns, which they had written in matrix form as Ax = b.
Nicholas reduced A to a row echelon form matrix U, but accidentally blurred out some of their work with blue cordial, leaving four of the entries
unreadable.
The row echelon form matrix now looks like
2
U =
6
(a)
Given only this information, select all options that give a possible geometrical description of the solutions of the system of equations.
the empty set
O a point
a line
O a plane
O all of R1
(b)
Leonardo remembers that three specific solutions for the system are
-2
3
and x=
10
-15
-21
-25
Nicholas says, "That's great! That means we can write a general solution to the system of equations in the form
x = a + tiv1 + tzv2
or perhaps as
x = a+ tiv1
for some vectors a, v1, V2 E R* and real parameters t, and tg.- Hmmmm, I'm not sure which, maybe we need even more vectors and parameters. Can
you help me?"
Find a parametric vector form of the solution to the system of equations Ax = b given the three specific solutions above and enter it in the box below the
syntax advice
Write your answer in Maple syntax and use parameter names of the form, t1, t2, t3 (as many as you need). For example, if this problem were in R.
typical solutions would look like
< 1, 2 > + t1*< 3, 4 > + t2*< 5, 6 >
or
< 1, 2 > + tl*< 3, 4 >](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1af2e839-a835-4130-9203-42e58df89277%2Fc4719952-5351-4c27-9240-7ce97d36ed14%2Fakz3zna_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Nicholas and Leonardo had been trying to solve a system of three equations in four unknowns, which they had written in matrix form as Ax = b.
Nicholas reduced A to a row echelon form matrix U, but accidentally blurred out some of their work with blue cordial, leaving four of the entries
unreadable.
The row echelon form matrix now looks like
2
U =
6
(a)
Given only this information, select all options that give a possible geometrical description of the solutions of the system of equations.
the empty set
O a point
a line
O a plane
O all of R1
(b)
Leonardo remembers that three specific solutions for the system are
-2
3
and x=
10
-15
-21
-25
Nicholas says, "That's great! That means we can write a general solution to the system of equations in the form
x = a + tiv1 + tzv2
or perhaps as
x = a+ tiv1
for some vectors a, v1, V2 E R* and real parameters t, and tg.- Hmmmm, I'm not sure which, maybe we need even more vectors and parameters. Can
you help me?"
Find a parametric vector form of the solution to the system of equations Ax = b given the three specific solutions above and enter it in the box below the
syntax advice
Write your answer in Maple syntax and use parameter names of the form, t1, t2, t3 (as many as you need). For example, if this problem were in R.
typical solutions would look like
< 1, 2 > + t1*< 3, 4 > + t2*< 5, 6 >
or
< 1, 2 > + tl*< 3, 4 >
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