Example of Kernel and Range of Linear Transformation

Linear Algebra: Find bases for the kernel and range for the linear transformation T:R^3 to R^2 defined by T(x1, x2, x3) = (x1+x2, -2x1+x2-x3). We solve by finding the corresponding 2 x 3 matrix A, and find its null space and column span. We check our work using the Rank Equation.

Category:

Education

Tags:

• Mathematics
• linear
• algebra
• matrix
• transformation
• kernel
• range
• null
• space
• column
• span
• rank
• equation
• formula

[lightmarepeno]

Do you work out or do you look like that naturally

[MathDoctorBob]

@lightmarepeno Weightlifter as a youngster, these days I do a lot of jiu-jitsu and grappling. I haven't touched a weight in over 10 years. - Bob

[MrKh0i]

@MathDoctorBob Olympic weightlifter?

[MathDoctorBob]

@MrKh0i Edit: My bad! I've been out of the weight room for too long. Our workouts were built around bench press, squats, and deadlifts with a lot of isolation work; more geared towards bodybuilding than powerlifting. We just wanted to get big, not necessarily strong or pretty. And nothing formal; we learned everything from Weider and Schwartzenegger's books back in the 80s. - Bob

[epocalipticify]

Thank you so much! I was struggling while reading my textbook with the content but you made it so understandable!

[MathDoctorBob]

@epocalipticify You're welcome! Different modes. Books are better for reference and thoroughness. With a video, I want to get across intuition and why you should care. - Bob

[Pasgo523]

Dr. Bob. You are our savior. we would rather watch your videos than go to our linear algebra class. we have a test in 11 hours and did not know anything before watching your collection of linear videos. You rock! Thank you again from SUNY Oneonta New York.

[T0mmm14]

Very clearly explained, thanks very much

[xcvxish]

Can you make videos on fourier transform plss. --Shoeb

[MathDoctorBob]

@f4bfour Thanks! - Bob

[MathDoctorBob]

@kev121314 I just caught this. I will put it in the queue. If this video makes sense, it is just translating.

1-1: null space is zero, or pivot in each column

onto: range spans the image R^n , or pivot in each row

-Bob