Solve 2x2 Matrix in 30 Mins: An Attempt

  • Thread starter Thread starter nicknaq
  • Start date Start date
  • Tags Tags
    Matrix
AI Thread Summary
The discussion focuses on finding the inverse of a given 2x2 matrix A using elementary matrices. The user attempts to express A^-1 as a product of four elementary matrices but realizes their solution is incorrect. They detail their row operations, including swapping rows and scaling, but seek clarification on the correct elementary matrix for a specific operation. The conversation highlights the importance of accurately applying row operations to achieve the desired matrix form. The user is looking for guidance to correct their approach and finalize the solution.
nicknaq
Messages
67
Reaction score
0
I really need an answer in the next 30 min.

Homework Statement


Given the 2x2 matrix A= 0 −2
9 −5
Write A^-1 as a product of 4 elementary matrices.

The Attempt at a Solution



I got the following. It's wrong. Please find my error.

1 0 | 1/9 0 | 1 0 | 1 5/9
0 1 | 0 1 | 0 -1/2 | 0 1

Edit: Geeze. the forum won't let me show the spaces between the four matrices above. sorry.
 
Physics news on Phys.org


After swapping the two rows, dividing the first row by 9, and dividing the second row by -2, you have row-reduced A to
\begin{bmatrix}1 & -5 \\ 0 & 1\end{bmatrix}
so you have to add 5 times the second row to the first row. What elementary matrix does that?
(You seem to have kept the "9" you got rid of with the second elementary matrix.)
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

A gardener collected 17 apples...
Replies
32
Views
2K
How Do You Find Eigenvectors of a 2x2 Matrix?
Replies
6
Views
2K
Problem with calculating eigen vector for 2*2 Matrix
Replies
5
Views
1K
Representing a transformation with a matrix
Replies
8
Views
2K
Problems in manipulating these 4 radical equations
Replies
8
Views
1K
Python Partial pivoting in getting the reduced row echelon form of a matrix
Replies
2
Views
1K
Expressing Matrix Power as linear combination
Replies
7
Views
3K
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
Replies
2
Views
1K
Solving an inequality involving absolute values
Replies
11
Views
2K
Matrix Space, dependence/indepence (HELP)
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top