Solve 2x2 Matrix in 30 Mins: An Attempt

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In summary, the conversation discusses finding the inverse of a 2x2 matrix by using elementary matrices. The attempted solution involves row operations and dividing rows, but an error is made in the final step where an extra 9 is included. The correct solution involves adding 5 times the second row to the first row.
  • #1
nicknaq
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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.
 
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  • #2


After swapping the two rows, dividing the first row by 9, and dividing the second row by -2, you have row-reduced A to
[tex]\begin{bmatrix}1 & -5 \\ 0 & 1\end{bmatrix}[/tex]
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.)
 

FAQ: Solve 2x2 Matrix in 30 Mins: An Attempt

How do you solve a 2x2 matrix?

To solve a 2x2 matrix, you will need to use a specific set of steps called the "Gaussian Elimination" method. This involves using elementary row operations to transform the matrix into an upper triangular form, and then solving for the unknown variables using back substitution.

Can a 2x2 matrix be solved in 30 minutes?

Yes, it is possible to solve a 2x2 matrix in 30 minutes if you are familiar with the necessary steps and have a good understanding of linear algebra. However, the time it takes to solve a matrix can vary depending on the complexity of the equations and the level of experience of the person solving it.

What is the purpose of solving a 2x2 matrix?

Solving a 2x2 matrix allows us to find the values of unknown variables in a system of linear equations. This is useful in various fields of science, such as physics and engineering, where systems of equations are used to model real-world situations and make predictions.

Are there any shortcuts to solving a 2x2 matrix?

Yes, there are some shortcuts or alternative methods that can be used to solve a 2x2 matrix, such as the Cramer's rule or the inverse matrix method. However, these methods may not always be applicable or efficient, and the Gaussian Elimination method is generally considered the most reliable and widely used approach.

What are some common mistakes to avoid when solving a 2x2 matrix?

Some common mistakes when solving a 2x2 matrix include forgetting to perform all the necessary row operations, making calculation errors, and not checking the final solution for accuracy. It is important to double-check each step and take your time to avoid making mistakes that could affect the accuracy of the solution.

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