Rotating Linear

Home > Lenses > Rotating Linear

October 4th, 2007 admin Leave a comment Go to comments

Rotating Linear

Vector Rotated Linear Algebra Question?

Does anyone have a good explanation to this problem? Thanks
Consider a vector (x,y) in R2 that is rotated 45 degrees clockwise, then reflected across the y axis, then projected on the x axis.
A) Find the matrix of T= T3 * T2 * T1 which accomplishes this.
B) Find the ker(T).

T1 will be the rotation matrix (note the minus sign, since the rotation is clockwise)
[ cos(-45) -sin(-45)] =
[ sin(-45) cos(-45)]

[1 1] * sqrt(2/2).
[-1 1]

T2 will be the reflection matrix
[1 0]
[0 -1]
(since T2(1,0) = (1,0) and T2(0,1) = (0,-1).)

T3 will be the projection matrix
[1 0]
[0 0]
(since T3(1,0) = (1,0) and T3(0,1) = (0,0).)

I’ll leave it to you to multiply these to get T.

As for Part B), just row reduce and set the matrix equal to the zero vector. Good luck!

Quantum cryptography protocol doesn`t require shared reference frames (Update)
(PhysOrg.com) — Quantum cryptography, which enables two parties to communicate with each other with unconditional security, has begun to be implemented by some governments, banks, and other corporations with high-security requirements. However, certain applications of quantum cryptography, such as satellite links, have proved to be challenging, partly due to a key requirement of quantum key …

Extech RPM10 Combination Tachometer with Infrared Thermometer

$309.99

Large 0.4″ (5 digit) LCD display. Non-contact Photo tachometer uses a Laser for greater measuring distance up to 6.5ft (2m). Contact tachometer for RPM and surface speed measurements. Memory stores Min/Max/Last. Characters on display reverse direction depending on mode. Double molded housing….

Linear Functions, Equations & Graphs

$29.99

TI graphing calculators are used to explore the nature of linear functions. Examples from air travel, environmental engineering, and space travel provide real-world examples for understanding this algebraic concept. Concepts explored include standard form, slope-intercept form, point-slope form, and solving linear equations. All examples are solved graphically and then reinforced through the use …