Help with Matrix Reduction: Q1 & Q2 Answers

• ivanyo
In summary, the conversation is about a person seeking help with matrix reduction. They have two questions, one about finding the inverse of a matrix and the other about solving a system of equations. The person provides images of their attempts but is stuck and asks for suggestions. Another person responds with tips and encourages the first person to check their solution. The first person is also advised to avoid writing fractions as mixed numbers for easier calculations.
ivanyo
Hi everyone!

I'm in need for some help with Matrix Reduction! I have two questions:

Question 1
Find the inverse of Matrix A by reducing the array (A|I), where
A=
2 4 6
4 5 5
3 1 -3

Question 2
Find all solutions of the following system:
2x1 + 4x2 + x3 - 3x4 - 3x5 = -5
x1 + 2x2 - x3 + 3x4 - 3x5 = -4
-2x3 + 7x4 - x5 = 0
x1 + 2x2 + x4 - x5 = -1The first two images are my attempt at question 1 - I get stuck and can't seem to get the identity matrix on the left. I know the answer (in red) through using a Matrix Calculator.

The last two images are my attempt at question two. I get stuck trying to find x2 and x1 using back substitution. Any suggestions?

*My apologies for the bad handwriting! Imgur is playing up and won't let me rotate the last 3 photos either :(
Image 1 - http://imgur.com/hXHhh
Image 2 - http://tinypic.com/view.php?pic=29kpg5l&s=7
Image 3 - http://tinypic.com/view.php?pic=9zrkex&s=7
Image 4 - http://tinypic.com/view.php?pic=33cxfuh&s=7Thanks for any help in advanced!

Last edited:
Bump! Need help asap!

For the 2nd one, you are going to have one free variable, so let x2 = t. Solve for x1 from that equation. With one free variable, the solution set is not a single point - it's all points on some line in R5.

When you're done, check that your solution satisfies the original system of equations. If so, then you're done.

I didn't look at the 1st problem very closely, but at this level of mathematics you should pretty much never write a fraction as a mixed number. For example, 5/3 is good but 1 2/3 is not good - it makes any further calculations more difficult.

1. What is matrix reduction?

Matrix reduction is the process of transforming a matrix into a simpler form by performing a series of operations, such as row operations and column operations. The goal of matrix reduction is to simplify the matrix and make it easier to solve or interpret.

2. Why is matrix reduction important in scientific research?

Matrix reduction is important in scientific research because it allows for complex data sets to be organized and analyzed. It also helps to identify patterns and relationships between variables, which can aid in making predictions and drawing conclusions from the data.

3. What are some common methods used for matrix reduction?

Some common methods used for matrix reduction include Gaussian elimination, LU decomposition, and QR decomposition. These methods involve performing a series of mathematical operations on the matrix to simplify it.

4. Can matrix reduction be applied to any type of matrix?

Yes, matrix reduction can be applied to any type of matrix, including square matrices, rectangular matrices, and even complex matrices. The methods used may vary depending on the type of matrix, but the overall goal of simplifying the matrix remains the same.

5. What are some real-world applications of matrix reduction?

Matrix reduction has many real-world applications, including in fields such as engineering, physics, economics, and computer science. It can be used for data analysis, solving systems of equations, and image processing, among other things.

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