Solving a Matrix: How to Go Further?

[Boom101]

A =
| 1 2 0 |
| 0 2h-6 h-2 |
| 0 1 1 |

How do I go further? 2h - 6 = 1? Or should it be (2h-6 times a constant x) = 1, and then write the answer in terms of x? I thought of also using x(2h-6) = 1, isolate x and replace it in x(h-2) = 0 to put the answer in terms of h. But I don't think it should be in terms of any variables. Help please!

 

[Mark44]

Homework Statement

A =
| 1 3 1 |
| 2 2h h |
|-3 -8 -2 |

Find all values of h so A is invertible. The thing is I cannot use determinants.

Homework Equations

Elementary Row Operations

The Attempt at a Solution

Now I attempted to make it reduced echelon form and got

A =
| 1 2 0 |
| 0 2h-6 h-2 |
| 0 1 1 |

But how do I go further? 2h - 6 = 1? Or should it be (2h-6 times a constant x) = 1, and then write the answer in terms of x? I thought of also using x(2h-6) = 1, isolate x and replace it in x(h-2) = 0 to put the answer in terms of h. But I don't think it should be in terms of any variables. Help please!

To get a 1 entry in the 2nd row, you need to divide by 2h - 6. Does that suggest a value that h cannot be?

 

[Dick]

To get a 1 entry in the 2nd row, you need to divide by 2h - 6. Does that suggest a value that h cannot be?

Careful. h=3 doesn't make the matrix singular. Exchange the second and third rows and keep reducing.

 

[Boom101]

Ok so I get h-2 / 2h-6 I still don't understand how to finish.

 

[Mark44]

After swapping the 2nd and 3rd rows, as Dick suggested, you should have this:
$$\left[ \begin{array}{c c c}<br /> 1 & 2 & 0 \\<br /> 0 & 1 & 1 \\<br /> 0 & 2h - 6 & h - 2 \end{array}<br /> \right]$$

Use the new 2nd row to eliminate the leading entry in the 3rd row. You should not get (h - 2)/(2h - 6).
As Dick suggested, swap the 2nd and 3rd rows.

 

[Boom101]

Thanks everyone for the help. How do I find values other than h = 3?

 

[Dick]

Thanks everyone for the help. How do I find values other than h = 3?

You'd better listen more closely to the help. h=3 is wrong. Swap the rows and finish the reduction. Then tell me what you get.