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Examine the consistency of the system of equation x + 2y = 2; 2x + 3y = 3
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Examine the consistency of the system of equation x + 2y = 2; 2x + 3y = 3

Answer

Matrix form of given equations is AX = B
\(\Rightarrow \left[ {\begin{array}{*{20}{c}} 1&2 \\ 2&3 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} x \\ y \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 2 \\ 3 \end{array}} \right]\)
\(\therefore A = \left[ {\begin{array}{*{20}{c}} 1&2 \\ 2&3 \end{array}} \right]\) and \(B = \left[ {\begin{array}{*{20}{c}} 2 \\ 3 \end{array}} \right]\)
\(\therefore \left| A \right| = \left| {\begin{array}{*{20}{c}} 1&2 \\ 2&3 \end{array}} \right| = 3 - 4 = - 1 \ne 0\)
Therefore, Unique solution and hence equations are consistent.
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