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IFT:R R² is a linear transformation given by Tix, y, z)=(x, y), Vix,y,ze R³ with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R². What is the matrix representation of T?
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IFT:R R² is a linear transformation given by Tix, y, z)=(x, y), Vix,y,...
Matrix Representation of T
To find the matrix representation of the linear transformation T with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R², we need to determine the images of the basis vectors (1,0,0), (0,1,0), and (0,0,1) under the transformation T.
Transformation of the Standard Basis
Let's first determine the images of the standard basis vectors under T:
T(1,0,0) = (1,0)
T(0,1,0) = (0,1)
T(0,0,1) = (0,0)
Representation with Respect to the Basis
Next, we need to express these images with respect to the basis [(1,0), (1,1)) of R². We can write the images as linear combinations of the basis vectors:
T(1,0,0) = 1*(1,0) + 0*(1,1) = (1,0)
T(0,1,0) = 0*(1,0) + 1*(1,1) = (1,1)
T(0,0,1) = 0*(1,0) + 0*(1,1) = (0,0)
Matrix Representation
The matrix representation of T is obtained by arranging the coefficients of the linear combinations as columns in a matrix:
| 1 0 0 |
| 0 1 0 |
This matrix represents the linear transformation T from R³ to R² with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R².
To find the matrix representation of the linear transformation T with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R², we need to determine the images of the basis vectors (1,0,0), (0,1,0), and (0,0,1) under the transformation T.
Transformation of the Standard Basis
Let's first determine the images of the standard basis vectors under T:
T(1,0,0) = (1,0)
T(0,1,0) = (0,1)
T(0,0,1) = (0,0)
Representation with Respect to the Basis
Next, we need to express these images with respect to the basis [(1,0), (1,1)) of R². We can write the images as linear combinations of the basis vectors:
T(1,0,0) = 1*(1,0) + 0*(1,1) = (1,0)
T(0,1,0) = 0*(1,0) + 1*(1,1) = (1,1)
T(0,0,1) = 0*(1,0) + 0*(1,1) = (0,0)
Matrix Representation
The matrix representation of T is obtained by arranging the coefficients of the linear combinations as columns in a matrix:
| 1 0 0 |
| 0 1 0 |
This matrix represents the linear transformation T from R³ to R² with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R².
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IFT:R R² is a linear transformation given by Tix, y, z)=(x, y), Vix,y,ze R³ with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R². What is the matrix representation of T?
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IFT:R R² is a linear transformation given by Tix, y, z)=(x, y), Vix,y,ze R³ with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R². What is the matrix representation of T? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about IFT:R R² is a linear transformation given by Tix, y, z)=(x, y), Vix,y,ze R³ with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R². What is the matrix representation of T? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for IFT:R R² is a linear transformation given by Tix, y, z)=(x, y), Vix,y,ze R³ with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R². What is the matrix representation of T?.
IFT:R R² is a linear transformation given by Tix, y, z)=(x, y), Vix,y,ze R³ with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R². What is the matrix representation of T? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about IFT:R R² is a linear transformation given by Tix, y, z)=(x, y), Vix,y,ze R³ with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R². What is the matrix representation of T? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for IFT:R R² is a linear transformation given by Tix, y, z)=(x, y), Vix,y,ze R³ with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R². What is the matrix representation of T?.
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IFT:R R² is a linear transformation given by Tix, y, z)=(x, y), Vix,y,ze R³ with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R². What is the matrix representation of T?, a detailed solution for IFT:R R² is a linear transformation given by Tix, y, z)=(x, y), Vix,y,ze R³ with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R². What is the matrix representation of T? has been provided alongside types of IFT:R R² is a linear transformation given by Tix, y, z)=(x, y), Vix,y,ze R³ with respect to the standard basis of R³ and the basis [(1,0), (1,1)) of R². What is the matrix representation of T? theory, EduRev gives you an
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