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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.
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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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