Assume that T is a linear transformation such that T: R2->R4, T(e1) T(e2)= [-5 2 0 0] a)Find the standard matrix of T b)Determine if the linear transformation is one-to-one or onto or I need both of them’s solutions.May you help me ? 
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Find all linear transformations $T$ from $\mathbb{R}^{2}$ to $\mathbb{R}^{2}$ such that $$T\left[\begin{array}{l} 1 \\ 2 \end{array}\right]=\left[\begin{array}{l} 2 \\ 1 \end{array}\right] \quad \text { and } \quad T\left[\begin{array}{l} 2 \\ 5 \end{array}\right]=\left[\begin{array}{l} 1 \\ 3 \end{array}\right].$$ Hint: We are looking for the $2 \times 2$ matrices $A$ such that \[A\left[\begin{array}{l} 1 \\ 2 \end{array}\right]=\left[\begin{array}{l} 2 \\ 1 \end{array}\right] \quad \text { and } \quad A\left[\begin{array}{l} 2 \\ 5 \end{array}\right]=\left[\begin{array}{l} 1 \\ 3 \end{array}\right].\] These two equations can be combined to form the matrix equation \[A\left[\begin{array}{ll} 1 & 2 \\ 2 & 5 \end{array}\right]=\left[\begin{array}{ll} 2 & 1 \\ 1 & 3 \end{array}\right].\]
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