Respuesta :
Answer:
(a) a=6 and b≠[tex]\frac{11}{4}[/tex]
(b)a≠6
(c) a=6 and b=[tex]\frac{11}{4}[/tex]
Step-by-step explanation:
writing equation in agumented matrix form
[tex]\begin{bmatrix}1 &1 & 0 &1 &b\\ 2 &3 & 1 &5 &6\\ 0& 0 & 1 &1 &4\\ 0& 2 & 2&a &1\end{bmatrix}[/tex]
now [tex]R_{2} =R_{2}-2\times R_{1}[/tex]
[tex]\begin{bmatrix}1 &1& 0 &1 &b\\ 0 &1& 1 &3 &6-2b\\ 0& 0 & 1 &1 &4\\ 0& 2 & 2&a &1\end{bmatrix}[/tex]
now [tex]R_{4} =R_{4}-2\times R_{2}[/tex]
[tex]\begin{bmatrix}1 &1& 0 &1 &b\\ 0 &1& 1 &3 &6-2b\\ 0& 0 & 1 &1 &4\\ 0& 0 & 0 &a-6 &4b-11\end{bmatrix}[/tex]
a) now for inconsistent
rank of augamented matrix ≠ rank of matrix
for that a=6 and b≠[tex]\frac{11}{4}[/tex]
b) for consistent w/ a unique solution
rank of augamented matrix = rank of matrix
a≠6
c) consistent w/ infinitely-many sol'ns
rank of augamented matrix = rank of matrix < no. of variable
for that condition
a=6 and b=[tex]\frac{11}{4}
then rank become 3 which is less than variable which is 4.
