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- Homework Statement
- Let T be the linear transformation from R3 into R2 defined by T(x1, x2, x3) = (x1 + x2, 2x3 - x1).

B={α1,α2,α3} and B′ ={β1,β2}, where α1 = (1,0,−1), α2 = (1,1,1), α3 = (1,0,0), β1 = (0,1), β2 = (1,0). What is the matrix of T relative to the pair B, B′?

- Relevant Equations
- transformation

T(α1), T(α2), T(α3) written in terms of β1, β2:

Tα1 =(1,−3)

Tα2 =(2,1)

Tα3 =(1,0).

Then there is row reduction:

Therefore, the matrix of T relative to the pair B, B' is

I don't understand why the row reduction takes place? Also, how do these steps relate to ## B = S^{-1}AS ##? Thank you.

Tα1 =(1,−3)

Tα2 =(2,1)

Tα3 =(1,0).

Then there is row reduction:

Therefore, the matrix of T relative to the pair B, B' is

I don't understand why the row reduction takes place? Also, how do these steps relate to ## B = S^{-1}AS ##? Thank you.

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