Answer: An elementary matrix E is one obtained by performing a single row operation on
Chapter 8, Problem 38(choose chapter or problem)
If a, b, and c are real numbers and \(c\ \neq\ 0\), then ac = bc implies a = b. For matrices, AC = BC, \(C\ \neq\ 0\), does not necessarily imply A = B. Verify this for
\(\mathbf{A}=\left(\begin{array}{lll} 2 & 1 & 4 \\ 3 & 2 & 1 \\ 1 & 3 & 2 \end{array}\right), \mathbf{B}=\left(\begin{array}{rrr} 5 & 1 & 6 \\ 9 & 2 & -3 \\ -1 & 3 & 7 \end{array}\right)\)
and
\(\mathbf{C}=\left(\begin{array}{lll} 0 & 0 & 0 \\ 2 & 3 & 4 \\ 0 & 0 & 0 \end{array}\right)\).
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