Select one or more: O a. The function R → R’ which maps a number x to the vector ū = (x, 2x, x²) O b. The function R → R which maps the vector ū = (v1, U2, U3) to the determinant U2 U3 of the matrix 1 2 3 4 5 6. O c. The function R → R which maps a vector ū = (v1, V2, V3) to vị + 2v2 ·
Select one or more: O a. The function R → R’ which maps a number x to the vector ū = (x, 2x, x²) O b. The function R → R which maps the vector ū = (v1, U2, U3) to the determinant U2 U3 of the matrix 1 2 3 4 5 6. O c. The function R → R which maps a vector ū = (v1, V2, V3) to vị + 2v2 ·
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
Which of the following are linear transformations?
Transcribed Image Text:Which of the following are linear transformations?
Select one or more:
a. The function R -
→ R' which maps a
number x to the vector ū = (x, 2x, x²)
O b. The function R3
vector ī = (v1, U2, U3) to the determinant
→ R which maps the
U2
U3
of the matrix
1
3
4
5
6.
O c. The function R3
ū = (v1, V2, V3) to v1 + 2v2.
→ R which maps a vector
d. The composition So T • S where T and S
are both linear transformation from
R"
→ R"
O e. The function R?
→ R² which first
orthogonally projects onto the line spanned
by (1, 2), and then translates by 2 in the x
direction.
O f. The function R to R which maps
X H x + 3
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