Solving for h in a Consistent Linear System

In summary, the conversation is about determining the value of h for a consistent linear system based on an augmented matrix. The participants discuss possible solutions and eventually come to the conclusion that h cannot be 15 for the system to be inconsistent.
  • #1
beanryu
92
0
hello.
please help!

this is the problem:
determine the value of h such that the matrix is the augmented matrix of a consistent linear system.

1 -3 -2
5 h -7

i tried replacing and scaling... but it seems there are always 2 variable in this.
can you guys help me solve this problem?
 
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  • #2
Is that an augmented system:

1x-3y=-2
5x+hy=-7

?
 
  • #3
is that not?
 
  • #4
is the answer any number... because with everynumber, there is a different solution to x and y?... probably true?
 
  • #5
ohkay... i think i got the answer... h cannot be 15, because than it will be

1 -3 -2
0 0 3
this show that it will be inconsistent...
 
  • #6
No, you've "lost a sign". The row reduction of
[tex]\left[\begin{array}{ccc}1 & -3 & -2 \\ 5 & h & 7\end{array}\right][/tex]
is
[tex]\left[\begin{array}{ccc}1 & -3 & 2\\ 0 &h+ 15 & 3\end{array}\right][/tex]

What must h be so that is inconsistent?
 

FAQ: Solving for h in a Consistent Linear System

What is a consistent linear system?

A consistent linear system is a set of equations that has at least one solution. This means that the equations can be solved simultaneously to find a unique value for each variable.

Why is solving for h important in a consistent linear system?

Solving for h allows us to find the unique solution to the system of equations. It represents the value of the variable h that satisfies all of the equations in the system.

What is the process for solving for h in a consistent linear system?

The process for solving for h involves using algebraic methods, such as substitution or elimination, to manipulate the equations so that h is isolated on one side of the equal sign. Once h is isolated, its value can be determined by solving the resulting equation.

What does it mean if a consistent linear system has no solution?

If a consistent linear system has no solution, it means that the set of equations cannot be satisfied simultaneously. This could be due to a mistake in the equations, or the equations may be inconsistent and have no solution.

Is there a specific method for solving for h in a consistent linear system?

No, there is no one specific method for solving for h in a consistent linear system. The method used will depend on the specific equations and variables involved. However, there are common algebraic techniques that can be applied, such as substitution, elimination, or using matrices.

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