Consider the set of vectors S= (u₁, U₂) in R³, where u₁ = (1,-1,2) and u₂ = (-2,0,3). Is the vector b= (12,-2,-11) a linear combination of the vectors in the set 57 If it is, write b as a linear combination of u, and u₂. If it is not, explain why. Show all necessary calculations. Does the set S span R³? in R², where T Given the linear transformation T: R² R³ defined by T(x) = Ax for all x 1-2 A = [U₁ U₂] -1 0 2 3 does T map R² onto R³? Circle your choice below and briefly justify your answer. Circle One: [Onto / Not onto
Consider the set of vectors S= (u₁, U₂) in R³, where u₁ = (1,-1,2) and u₂ = (-2,0,3). Is the vector b= (12,-2,-11) a linear combination of the vectors in the set 57 If it is, write b as a linear combination of u, and u₂. If it is not, explain why. Show all necessary calculations. Does the set S span R³? in R², where T Given the linear transformation T: R² R³ defined by T(x) = Ax for all x 1-2 A = [U₁ U₂] -1 0 2 3 does T map R² onto R³? Circle your choice below and briefly justify your answer. Circle One: [Onto / Not onto
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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![Consider the set of vectors S= {u₁, U₂) in R³, where u₁ = (1,-1,2) and u₂ = (-2,0,3).
Is the vector b= (12,-2, -11) a linear combination of the vectors in the set S?
If it is, write b as a linear combination of u, and u₂. If it is not, explain why. Show all necessary
calculations.
Does the set S span R³?
I
in R², where
Given the linear transformation T: R² R³ defined by T(x) = Ax for all x
A = [u₁ U₂]
1-2
0
3
-1
2
does T map R² onto R³? Circle your choice below and briefly justify your answer.
Circle One: [Onto / Not onto](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6e6d380-54a4-46c8-adc0-56f54d5d0909%2Fe5e514ff-59f6-4689-9f82-d73a5bc079d7%2Fm2pf0sg_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the set of vectors S= {u₁, U₂) in R³, where u₁ = (1,-1,2) and u₂ = (-2,0,3).
Is the vector b= (12,-2, -11) a linear combination of the vectors in the set S?
If it is, write b as a linear combination of u, and u₂. If it is not, explain why. Show all necessary
calculations.
Does the set S span R³?
I
in R², where
Given the linear transformation T: R² R³ defined by T(x) = Ax for all x
A = [u₁ U₂]
1-2
0
3
-1
2
does T map R² onto R³? Circle your choice below and briefly justify your answer.
Circle One: [Onto / Not onto
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