[See] (a) What does the matrix E_2^1=(ll0 1 , 1 0) do to M=(lla b , d c) under left multiplication? What about right multiplication? (b) Find elementary


Question: (a) What does the matrix \(E_{2}^{1}=\left(\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right)\) do to \(M=\left(\begin{array}{ll}a & b \\ d & c\end{array}\right)\) under left multiplication? What about right multiplication?

(b) Find elementary matrices \(R^{1}(\lambda)\) and \(R^{2}(\lambda)\) that respectively multiply rows 1 and 2 of \(M\) by \(\lambda\) but otherwise leave \(M\) the same under left multiplication.

(c) Find a matrix \(S_{2}^{1}(\lambda)\) that adds a multiple \(\lambda\) of row 2 to row 1 under left multiplication.

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