Help, I need the following question about matrices solved

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In summary, matrices are used in scientific research to represent and analyze complex data sets, equations, and systems. To solve a matrix, you need to use mathematical operations such as addition, subtraction, multiplication, and division to manipulate the elements. The dimensions of a matrix are determined by the number of rows and columns it contains, and there is a difference between square and non-square matrices in terms of their usage and operations. Not all mathematical operations can be performed on matrices, and certain operations are limited to square matrices only.
  • #1
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Homework Statement



Find the image location of point (5,2) after reflection in the x-axis followed by rotation through 180 degrees about the origin.

Homework Equations



Matrix Transformation

The Attempt at a Solution



None, need help!
 
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  • #2
Well, can you do the first part of the question? (ie. the reflection)
 
  • #3
I know that the matrix A which represents reflection in the x-axis is:

1 0
0 -1

But don't really know anything else about solving this question as it's all new to me...
 
  • #4
Forget about the matrix representation for now...

What is the image of (5,2) reflected on the x-axis?
 
  • #5


Sure, I would be happy to assist you with this problem. Let's start by breaking down the steps of the transformation.

First, we need to reflect the point (5,2) in the x-axis. This means that the y-coordinate will stay the same, but the x-coordinate will become its negative value. So, after reflection, the point becomes (-5,2).

Next, we need to rotate the point through 180 degrees about the origin. This means that both the x and y coordinates will become their negative values. So, after rotation, the point becomes (-(-5), -2), which simplifies to (5,-2).

To represent these transformations using matrices, we can use the following matrices:

Reflection in the x-axis:
[1 0]
[0 -1]

Rotation through 180 degrees:
[-1 0]
[ 0 -1]

To find the final image location, we need to multiply these two matrices together and then multiply it by the original point (5,2).

So, the final matrix transformation would be:
[-1 0] [1 0] [5] [-1 0] [5] [-5]
[ 0 -1] x [0 -1] x [2] = [ 0 -1] x [2] = [ 0]
[ 0] [-2]

Therefore, the image location of the point (5,2) after reflection in the x-axis followed by rotation through 180 degrees about the origin is (-5,-2). I hope this helps! Let me know if you have any further questions.
 

1. How do I solve a matrix?

To solve a matrix, you need to use a combination of mathematical operations such as addition, subtraction, multiplication, and division to manipulate the elements of the matrix. This will result in a simplified matrix with a specific value or set of values.

2. What is the purpose of using matrices in scientific research?

Matrices are used in scientific research to represent and analyze complex data sets, equations, and systems. They allow for efficient manipulation and calculation of large amounts of data, making them useful in various fields such as physics, engineering, and computer science.

3. How do I determine the dimensions of a matrix?

The dimensions of a matrix are determined by the number of rows and columns it contains. To find the dimensions, simply count the number of rows and columns in the matrix and write it in the format "m x n", where m is the number of rows and n is the number of columns.

4. What is the difference between a square matrix and a non-square matrix?

A square matrix has an equal number of rows and columns, while a non-square matrix has a different number of rows and columns. Square matrices are used for specific operations such as finding determinants and inverses, while non-square matrices are used for general calculations and data representation.

5. Can I perform all mathematical operations on matrices?

No, not all mathematical operations can be performed on matrices. Matrices must have the same dimensions to be added or subtracted, and they must follow specific rules for multiplication and division. Additionally, certain operations such as finding determinants and inverses can only be performed on square matrices.

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