Question

Let $T_1: \mathbb{R}^2 \to \mathbb{R}^2$ and $T_2: \mathbb{R}^2 \to \mathbb{R}^2$ be linear transformations defined as follows. $T_1 \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} -4x_1 \\ -5x_1 + 3x_2 \end{bmatrix}$ $T_2 \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} -3x_1 \\ 4x_2 \end{bmatrix}$ $(T_1 \circ T_2) \begin{bmatrix} -4 \\ 5 \end{bmatrix} = \begin{bmatrix} \text{Ex: 42} \\ \\ \end{bmatrix}$ $(T_2 \circ T_1) \begin{bmatrix} -4 \\ 5 \end{bmatrix} = \begin{bmatrix} \text{Ex: 42} \\ \\ \end{bmatrix}$

          Let $T_1: \mathbb{R}^2 \to \mathbb{R}^2$ and $T_2: \mathbb{R}^2 \to \mathbb{R}^2$ be linear transformations defined as follows.

$T_1 \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} -4x_1 \\ -5x_1 + 3x_2 \end{bmatrix}$

$T_2 \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} -3x_1 \\ 4x_2 \end{bmatrix}$

$(T_1 \circ T_2) \begin{bmatrix} -4 \\ 5 \end{bmatrix} = \begin{bmatrix} \text{Ex: 42} \\  \\ \end{bmatrix}$

$(T_2 \circ T_1) \begin{bmatrix} -4 \\ 5 \end{bmatrix} = \begin{bmatrix} \text{Ex: 42} \\  \\ \end{bmatrix}$

Let T1: ℝ^2 →ℝ^2 and T2: ℝ^2 →ℝ^2 be linear transformations defined as follows.

T1
< b m a t r i x >
=
< b m a t r i x >

T2
< b m a t r i x >
=
< b m a t r i x >

(T1 ∘ T2)
< b m a t r i x >
=
< b m a t r i x >

(T2 ∘ T1)
< b m a t r i x >
=
< b m a t r i x >

Added by Rebecca O.

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