Viewing the determinant of the transformation matrix as a scaling factor of regions Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/matrix_transpose/v/linear-algebra-transpose-of-a-matrix?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-and-area-of-a-parallelogram?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. ... https://www.youtube.com/watch?v=g3MqSdO5Ubc Note: All Khan Academy content is available for free at (www.khanacademy.org)

Naomi needs some help counting the number of blocks she walks from home to school. We'll use the coordinate plane to graph it out first. Let's go. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-geometry-topic/cc-5th-coordinate-plane/e/coordinate-plane-word-problems-in-the-first-quadrant?utm_source=YT&utm_medium=Desc&utm_campaign=5thgrade Watch the next lesson: https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-geometry-topic/cc-5th-quadrilaterals/v/quadrilateral-overview?utm_source=YT&utm_medium=Desc&utm_campaign=5thgrade Missed the previous lesson? https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-geometry-topic/cc-5th-coordinate-plane/v/graphing-points-exercise?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.) ... https://www.youtube.com/watch?v=_QKR8I5VE-w Note: All Khan Academy content is available for free at (www.khanacademy.org)

A worked example of computing and interpreting two-dimensional curl. ... https://www.youtube.com/watch?v=cAAEMza4GvQ Note: All Khan Academy content is available for free at (www.khanacademy.org)

Examples are very powerful tools! As writers, we can use them to make arguments stronger. As readers, we're engaged in a push-and-pull with writers, and have to think critically about how examples are used in a text. Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today! Donate here: https://www.khanacademy.org/donate?utm_source=youtube&utm_medium=desc Volunteer here: https://www.khanacademy.org/contribute?utm_source=youtube&utm_medium=desc ... https://www.youtube.com/watch?v=g9qWsEJakbQ Note: All Khan Academy content is available for free at (www.khanacademy.org)