Trouble with Inverse Matrices - Can You Help?

In summary, the conversation discusses using inverse matrices and multiplication with the identity matrix in order to solve a problem with a large matrix. The speaker also mentions the importance of using row operations and mentions a potential goal of finding the norm of certain columns.
  • #1
Geminiben
1
0

Homework Statement


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Homework Equations


I think it may have to do with inverse matrices or multiplication using the identity matrix

The Attempt at a Solution



I got the inverse of...

1,-2, 2, 2,-3
3,-5, 6, 2,-4
2,-2, 5,-4, 4
1,-3, 1, 7,-8
3,-4, 7, 0, 2

as...

-6,-14,25,20,-7
2,-13,19,14,-5
4, -2, 1, 0, 0
0, -1, 1, 1, 0
-1, 2 ,-3,-2, 1

and I premultiplied that to...

87, 57, 10,117,-101
208,232,133,330,-146
83,297,235,229, 116
154,-58,-97,112,-245
240,382,278,370, 092

But nothing really seems to make sense. Thanks if you can help!
 
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  • #2
It looks to me like it's one big giant matrix and you'd have to do the row operations to get the first 5 columns in the identity format and see what that does to the last 5 columns.
Are you looking for the norm of columns 6-10? The question isn't entirely clear to me.
 
Last edited:
  • #3
Yes, you have to do raw, direct calculations. But the semi-identity matrix will make it easier
 

1. What is an inverse matrix?

An inverse matrix is the reciprocal of a matrix. It is a mathematical operation that involves finding a matrix that when multiplied by the original matrix results in an identity matrix. The inverse matrix is used to solve equations and perform other mathematical operations.

2. Why is finding the inverse matrix important?

Finding the inverse matrix is important because it allows us to solve equations that involve matrices. It is also used in various mathematical operations such as matrix division and finding the determinant of a matrix.

3. How do you find the inverse matrix?

To find the inverse matrix, you can use the Gauss-Jordan elimination method or the adjugate method. In the Gauss-Jordan method, you perform row operations on the original matrix until it becomes an identity matrix. In the adjugate method, you use the adjugate matrix and the determinant of the original matrix to find the inverse.

4. Can every matrix have an inverse?

No, not every matrix can have an inverse. A matrix must be square (number of rows and columns are equal) and non-singular (determinant is not equal to 0) to have an inverse.

5. What are some common errors when finding the inverse matrix?

Some common errors when finding the inverse matrix include forgetting to switch the position of the original matrix and the identity matrix when using the Gauss-Jordan method, miscalculating the determinant or adjugate matrix, and not properly simplifying the final inverse matrix.

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