Question

Explain why the first column of the matrix is [1 0 0

]T NOT [ 1 0]T since the matrix is
2 by 2, please.
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B=\left[\left[T\left(\vec{v}_{1}\right)\right]_{y} ....\left[T\left(\vec{v}_{n}\right)\right]_{y}\right] \), where, \mathcal{B}=\left(\vec{v}_{1}, \vec{v}_{2}, .... \vec{v}_{n}\right) \) is

Answer 1

The first column of the matrix is [1 0 0]ᵀ, not [1 0]ᵀ because the matrix is 2 by 2.

Matrix Representation

In linear algebra, we often represent linear transformations as matrices. The given matrix B represents a linear transformation T in a certain basis