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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
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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Which of the following are linear transformations?

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
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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