prove that following system of linear equation has unique solution

Question : Prove that following system of linear equation has unique solution x+2y+3z=1, 2x+y+3z=2, 5x+5y+9z=4 Solution : Given system of linear equations x+2y+3z=1, 2x+y+3z=2, 5x+5y+9z=4 Matrix form AX =B \[\left(\begin{matrix}1&2&3\\2&1&3\\5&5&9\\\end{matrix}\right)\left(\begin{matrix}x\\y\\z\\\end{matrix}\right)=\left(\begin{matrix}1\\2\\4\\\end{matrix}\right)\] Augmented matrix \[\left[A:B\right]=\left(\begin{matrix}1&2&3&1\\2&1&3&2\\5&5&9&4\\\end{matrix}\right)\] Row reduce Echelon form of [A:B] \[\left[A:B\right]~\left(\begin{matrix}1&0&0&0\\0&1&0&-1\\0&0&1&1\\\end{matrix}\right)\]…

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