Henry Ernest Dudeney/Puzzles and Curious Problems/2 - A Legacy Puzzle/Working

== Working for by : $2$ -- 2 - A Legacy Puzzle ==

The simultaneous equations in matrix form:


 * $\begin {pmatrix}

1 & 1 &  1 &  1 \\ 1 & -1 & -1 &  1 \\ -2 &  1 & -2 &  1 \\ -3 & -3 &  1 &  1 \\ \end {pmatrix} \begin {pmatrix} a \\ b \\ c \\ h \end {pmatrix} = \begin {pmatrix} 1320 \\ 0 \\ 0 \\ 0 \end {pmatrix}$

when converted to reduced echelon form, gives:
 * $\begin {pmatrix}

1 & 0 & 0 &  0 \\ 0 & 1 &  0 &  0 \\ 0 & 0 &  1 &  0 \\ 0 & 0 &  0 &  1 \end {pmatrix} \begin {pmatrix} a \\ b \\ c \\ h \end {pmatrix} = \begin {pmatrix} 55 \\ 275 \\ 385 \\ 605 \\ \end {pmatrix}$