with problem with matrices, reflections, rotations

In summary, the given matrix for a reflection about the line y=-x is equivalent to a reflection relative to the y-axis followed by a counter-clockwise rotation of 90 degrees. To find the combined matrix, multiply the matrix for rotation with the matrix for reflection.
  • #1
dellatorre
5
0
Looking for help with a problem I'm working on:

"Show that matrix
[0 -1 0]
[-1 0 0]
[0 0 1]
for a reflection about line y=-x
is equivalent to a reflection relative to the y-axis followed by a counter-clockwise rotation of 90 degrees."

So for my answer, first I have for the reflection relative to the y axis, I have the matrix:
[-1 0 0]
[0 1 0]
[0 0 1]

and for the counter-clockwise rotation of 90 degrees, I have the matrix:
[0 -1 0]
[1 0 0]
[0 0 1]

but then I don't know what my next step should be.

Can anyone help me with this?

thanks,
Della
 
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  • #2
Sure. The matrix of the combined operation is the product of the matrices for the individual operations. Multiply (matrix of rotation)*(matrix of reflection).
 
  • #3
thank you
 

Related to with problem with matrices, reflections, rotations

What are matrices and how are they used in science?

Matrices are arrays of numbers, symbols, or expressions arranged in rows and columns. They are used in science to represent and manipulate data, equations, and transformations such as reflections and rotations.

What is a reflection and how is it performed using matrices?

A reflection is a transformation that flips a figure over a line of symmetry. To perform a reflection using matrices, the coordinates of each point in the figure are multiplied by a reflection matrix, which is a special type of matrix that has 1s and -1s in specific positions.

What is a rotation and how is it performed using matrices?

A rotation is a transformation that turns a figure around a fixed point. To perform a rotation using matrices, the coordinates of each point in the figure are multiplied by a rotation matrix, which is a special type of matrix that uses trigonometric functions to calculate the new coordinates.

How do matrices help solve problems in science?

Matrices are useful in solving problems in science because they provide a systematic way of organizing and manipulating data and equations. They also allow for complex transformations, such as reflections and rotations, to be easily performed and analyzed.

What are some common applications of matrices in science?

Matrices are used in various fields of science, including physics, chemistry, biology, and engineering. Some common applications include analyzing data in genetics and population dynamics, solving systems of equations in physics and chemistry, and performing transformations in computer graphics and image processing.

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