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.

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

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

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

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