Vector Multiplication Using Matrices (Assignment + Quiz)

Using both the rotation matrices earlier in this lesson and your matrix calculator, find each determinant.

1 1

Choose the correct choice for the matrix after applying the transformation to the triangle:

A

The diagram below shows vector v. Given transformation matrix T = [2 0 0 2], which diagram shows the application of T to v?

A

The diagram below shows vector v. If T = [0 1 1 0] is a transformation matrix, which expression correctly applies T to v?

A

The diagram below shows rectangle ABCD. Which points are in the image of rectangle ABCD under the transformation T = [3 0 0 3]

A (3,9)

All of these reflections resulted in ____________ figures.

congruent

Repeat this process for the other three matrices. The product of a reflection matrix and its transpose is the

identity matrix

please pass the favor forward

make these quizlets for others to help them out as well ^-^

Det R = ___________, which matches the determinant for our other ____________

r = 1 (sorry missed the next part)

The transformation T = [0 -1 -1 0] is applied the figure below. What type of transformation of triangle ABC was applied by T?

reflect across the line y = -x

Find the following determinant by hand.

1

Which transformation matrix would result in a 270° counterclockwise rotation about the origin?

B. [0 1 -1 0]

Find the product of the matrix and its transpose: R·Rt is

the identity matrix

Find the determinant of each of these. The determinant of each of these is

-1

Now find the following: A • At = ab cd where At is the transform of A.

1 0 0 1

The graph below shows the transformation from triangle 1 to triangle 2. Which sequence of steps would transform triangle 1 to triangle 2?

A. reflect across the y-axis; rotate 180° counterclockwise about the origin

Triangle ABC is shown below. Which point is the coordinate of the image of A under the transformation [0 -1 1 0]?

B. (-4, 2)

Which transformation matrix would result in a 300° counterclockwise rotation about the origin?

B. [1/2

Triangle ABC is shown below. Which point is the coordinate of the image of A under the transformation [0 1 1 0]?

C. (4, 2)

The diagram below shows vector v. Given transformation matrix T = [0 -1 -1 0], which diagram shows the application of T to v?

D

In mathematics, a pattern may suggest a conclusion, but it is not proof of it. Next you will prove that the determinant of a rotation matrix (CCW about the origin) must be 1. Luckily, there is the general rotation matrix you can use.

cos^2(x) + sin^2(x)

The resulting matrix creates an image that is _____________ to the original triangle.

not similar