You & maths

Exercise Set 1.1 – No. 5

5. Fnd a linear system in the unknowns x1,x2,x3,…, that corresponds to the given augmented matrix.

\large {\color{Blue} (a) \begin{bmatrix} 2 & 0 & 0 \\ 3 & -4 & 0 \\ 0 & 1 & 1 \end{bmatrix} }

\large {\color{Blue} (b) \begin{bmatrix} 3 & 0 & -2 & 5\\ 7 & 1 & 4 & -3\\ 0 & -2 & 1 & 7 \end{bmatrix} }

Since these are augmented matrices, the final column of an m x n matrix
is always the solution to \large {\color{Blue} a_{ij}x_1+a_{ij+1}x_2+... a_{in}x_n=b_i}. The coefficients
of are all of the numbers to the left of the final column, with each row
representing a single linear equation.

\large \\ (a)\; 2x_1=0,\;3x_1-4x_2=0,\;x_2=1 \\ (b)\; 3x_1-2x_3=5,\;7x_1+x_2+4x_3=-3,\;-2x_2+x_3=7 \\ (c)\; 7x_1+2x_2+x3-3x_4=5,\; x_1+2x_2+4x_3=1 \\ (d)\; x_1=7,\; x_2=-2,\; x3=3,\; x4=4