Solution Found!
Determine h and k such that the solution set of the system
Chapter , Problem 5E(choose chapter or problem)
Determine h and k such that the solution set of the system (i) is empty, (ii) contains a unique solution, and (iii) contains infinitely many solutions.
a. \(x_{1}+3 x_{2}=k\)
\(4 x_{1}+h x_{2}=8\)
b. \(-2 x_{1}+h x_{2}=1\)
\(6 x_{1}+k x_{2}=-2\)
Questions & Answers
QUESTION:
Determine h and k such that the solution set of the system (i) is empty, (ii) contains a unique solution, and (iii) contains infinitely many solutions.
a. \(x_{1}+3 x_{2}=k\)
\(4 x_{1}+h x_{2}=8\)
b. \(-2 x_{1}+h x_{2}=1\)
\(6 x_{1}+k x_{2}=-2\)
ANSWER:Solution Step 1:Given system of equations(a) We have to determine h and k such that the solution set of the system (i) is empty, (ii) contains a unique solution, and (iii) contains infinitely many solutions.First we need to find the reduced row echelon form of the augmented matrix of the linear system,Consider the system of equation in the form Ax=b Then the the reduced row echelon form of the augmented matrix we find