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Consider the following applications: I. T: R³ R², such that T(x, y, z) = (10z, x + y) II. S: R³ → R, such that T(x, y, z) = (x² +10y² + x²) III. R: M(3, R) → M(3, R) such that T(A) = A'A Then, which option is certain? Remark: 1T represents the linear transformation T a. T and R are linear transformations. b. S and 1T are linear transformations. c. They are all linear transformations. d. Only T is linear transformation.

Consider the following applications: I. T: R³ R², such that T(x, y, z) = (10z, x + y) II. S: R³ → R, such that T(x, y, z) = (x² +10y² + x²) III. R: M(3, R) → M(3, R) such that T(A) = A'A Then, which option is certain? Remark: 1T represents the linear transformation T a. T and R are linear transformations. b. S and 1T are linear transformations. c. They are all linear transformations. d. Only T is linear transformation.

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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Consider the following applications: I. T: R³ R², such that T(x, y, z) = (10z, x + y) II. S: R³ → R, such that T(x, y, z)=(x²+10y²+x²) III. R: M(3, R) → M(3, R) such that T(A) = A'A Then, which option is certain? Remark: 1T represents the linear transformation T a. T and R are linear transformations. b. S and 1T are linear transformations. c. They are all linear transformations. d. Only T is linear transformation.
Transcribed Image Text:Consider the following applications: I. T: R³ R², such that T(x, y, z) = (10z, x + y) II. S: R³ → R, such that T(x, y, z)=(x²+10y²+x²) III. R: M(3, R) → M(3, R) such that T(A) = A'A Then, which option is certain? Remark: 1T represents the linear transformation T a. T and R are linear transformations. b. S and 1T are linear transformations. c. They are all linear transformations. d. Only T is linear transformation.
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