What happens when finding an inverse of a matrix the determinant is 0?

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whispyr

New member
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Aug 3, 2012
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6
example:
[1 4 6]
[2 -3 1]
[-1 18 16]

does the inverse not exist if the determinant is 0?
 
whispyr said:
[h=2]What happens when finding an inverse of a matrix the determinant is 0?[/h]
Click to expand...

Nothing happens, beyond the discovery itself. Is there something specific that you're thinking might happen? ;)


does the inverse not exist if the determinant is 0?
Click to expand...

Yes.

A determinant value of zero tells us that the matrix has no inverse.
 
So the [1 4 6 : 1 0 0]
[2 -3 1:0 1 0]
[-1 18 16:0 0 1]

wouldn't apply to this scenario? I know how to line it up but then transferring everything over is something i'm a bit fuzzy on doing. Was just wondering if its asking for the inverse if it didn't exist or you had to use this method.
 
Code: 
[ 1   4   6  :  1  0  0]
[ 2  -3   1  :  0  1  0]
[-1  18  16  :  0  0  1]

You stated that you're fuzzy on transferring something over; I'm not sure what you're trying to say.

Did you yet try row operations on the augmented matrix above, to convert the matrix on the left into reduced-row echelon form? Try, and see what happens. (It won't work out.) :cool:

The matrix on the left is what we call a "singular" or "degenerate" matrix. It has no inverse. Checking whether its determinant is zero is a short-cut to realizing that there is no inverse (versus applying all of those row operations to eventually come to the same realization).


whispyr said:
Was just wondering if [it's] asking for the inverse if it didn't exist.
Click to expand...


You have used the same pronoun to reference different nouns; I cannot resolve your English.

If you have been given a question, please post it verbatim, so that I may see what you're talking about. Cheers.
 
Just thought there was going to be some tricky way to solve the problem :) over thinking I guess. Thank you for the clarification.
 
whispyr said:
So the [1 4 6 : 1 0 0]
[2 -3 1:0 1 0]
[-1 18 16:0 0 1]

wouldn't apply to this scenario? I know how to line it up but then transferring everything over is something i'm a bit fuzzy on doing. Was just wondering if its asking for the inverse if it didn't exist or you had to use this method.
Click to expand...

Are you trying to solve the equation \(\displaystyle \begin{bmatrix} 1 & 4 & 6 \\ 2 & -3 & 1 \\ -1 & 18 & 16\end{bmatrix}\begin{bmatrix}a & b & c \\ d & e & f \\ g & h & i\end{bmatrix}= \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}\)

Because the matrix does not have an inverse, the equation does not have a unique solution. That means that it either has NO solution or has an infinite number of solutions. You determine which by "row reducing" the augmented matrix you give. Because the matrix has no inverse, you will reduce to a matrix in which at least the last row (the first three numbers of the augmented matrix) will be all zeros. If there are any non-zero numbers in the last three places, there will be no solution. If the entire row is non-zero, there will be an infinite number of solutions.
 
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