Transpose of a matrix
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-determinant-of-transpose?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-as-scaling-factor?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=2t0003_sxtU
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Given the values of f and f' at x=-1 and that g(x)=2x_, Sal evaluates the derivative of F(x)=f(x)/g(x) at x=-1.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-rules/ab-quotient-rule/e/quotient_rule?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-rules/ab-rational-func-diff/v/rational-functions-differentiation?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-rules/ab-quotient-rule/v/quotient-rule?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
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https://www.youtube.com/watch?v=ZAElYVh5DXU
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Here's a great way to visualize fraction multiplication problems. Once you understand this, doing them on your own will be a lot easier!
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-fractions-topic/cc-5th-multiplying-fractions/e/multiplying_fractions_0.5?utm_source=YT&utm_medium=Desc&utm_campaign=5thgrade
Watch the next lesson: https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-fractions-topic/cc-5th-multiplying-fractions/v/concept-fraction-mult-number-line?utm_source=YT&utm_medium=Desc&utm_campaign=5thgrade
Missed the previous lesson? https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-fractions-topic/cc-5th-multiplying-fractions/v/multiplying-fractions?utm_source=YT&utm_medium=Desc&utm_campaign=5thgrade
Grade 5th on Khan Academy: Whether you are a robot, possum, magic unicorn, or just a normal human being, 5th grade is incredible! You will deepen your knowledge of the decimals that you were first exposed to in 4th grade. In particular, you'll learn to do all the arithmetic operations--addition, subtraction, multiplication, division--with them and really understand what a decimal represents. This will be complemented by building your fraction muscles where you'll learn to add, subtract, and multiply any fractions (and begin to divide them). On the measurement front, you'll explore volume (or how much "space" something takes up) and continue the unit conversion journey begun in 4th grade. 5th grade is also the first time that you get exposed to the fundamental concept of graphing points on a coordinate plane, and you'll get a very brief exposure to the concept of exponents (when exploring "powers" of 10)! (Content was selected for this grade level based on a typical curriculum in the United States.)
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https://www.youtube.com/watch?v=hr_mTd-oJ-M
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Example modeling asteroid velocity with differential equation
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https://www.youtube.com/watch?v=Ugwg2dHUB90
Note: All Khan Academy content is available for free at (www.khanacademy.org)
U03_L2_T2_we4 Dividing Decimals 2
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https://www.youtube.com/watch?v=D_E4Jws71rE
Note: All Khan Academy content is available for free at (www.khanacademy.org)
E2 E1 Sn2 Sn1 Reactions Example 2
More free lessons at: http://www.khanacademy.org/video?v=vinEPfrqfiU
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https://www.youtube.com/watch?v=vinEPfrqfiU
Note: All Khan Academy content is available for free at (www.khanacademy.org)
We are going live with Sal Khan this Thursday at noon PT / 3 pm ET! ⏰ Join us for Homeroom with Sal - be a part of our community and ask questions. Hope to see you soon!
For more information visit: keeplearning.khanacademy.org
Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. If you’d like to contribute, please visit:
https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=live&utm_campaign=schoolclosers
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https://www.youtube.com/watch?v=P6DKlpS58NE
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Let's take some complex looking fractions and make them much, much simpler.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-mult-div-fractions-2/e/complex-fractions?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade
Watch the next lesson: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-mult-div-fractions-2/v/rational-number-expressions?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade
Missed the previous lesson?
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-mult-div-fractions-2/v/dividing-mixed-numbers?utm_source=YT&utm_medium=Desc&utm_campaign=7thgrade
Grade 7th on Khan Academy: 7th grade takes much of what you learned in 6th grade to an entirely new level. In particular, you'll now learn to do everything with negative numbers (we're talking everything--adding, subtracting, multiplying, dividing, fractions, decimals... everything!). You'll also take your algebraic skills to new heights by tackling two-step equations. 7th grade is also when you start thinking about probability (which is super important for realizing that casinos and lotteries are really just ways of taking money away from people who don't know probability) and dig deeper into the world of data and statistics. Onward! (Content was selected for this grade level based on a typical curriculum in the United States.)
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https://www.youtube.com/watch?v=K2b8iMPY11I
Note: All Khan Academy content is available for free at (www.khanacademy.org)
In this video, Aspen Institute President and CEO Walter Isaacson talks to Sal about the background to the Declaration of Independence. Created by Sal Khan and Aspen Institute.
Watch the next lesson: https://www.khanacademy.org/humanities/us-history/road-to-revolution/declaration-of-independence/v/all-men-are-created-equal?utm_source=YT&utm_medium=Desc&utm_campaign=UShistory
Missed the previous lesson? https://www.khanacademy.org/humanities/us-history/road-to-revolution/benjamin-franklin/v/franklin-diplomat?utm_source=YT&utm_medium=Desc&utm_campaign=UShistory
US history on Khan Academy: From a mosquito-ridden backwater to the world's last remaining superpower, the United States of America is a nation with a rich history and a noble goal: government of the people, by the people, for the people. Its citizens' struggle to achieve that goal is a dramatic story stretching over hundreds of years.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=er1L9BB6UoE
Note: All Khan Academy content is available for free at (www.khanacademy.org)