The determinant of an upper triangular matrix Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-simpler-4x4-determinant?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-after-row-operations?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=VX7K8iqoiRc Note: All Khan Academy content is available for free at (www.khanacademy.org)

... https://www.youtube.com/watch?v=d4UQFgAdxUs Note: All Khan Academy content is available for free at (www.khanacademy.org)

26-30, area, circumference, pythagorean theorem Watch the next lesson: https://www.khanacademy.org/math/geometry/geometry-worked-examples/v/ca-geometry-area-circumference-volume?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Missed the previous lesson? https://www.khanacademy.org/math/geometry/geometry-worked-examples/v/ca-geometry-triangles-and-parallelograms?utm_source=YT&utm_medium=Desc&utm_campaign=Geometry Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry. 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=jRrRqMJbHKc

Interest groups and lobbying. NAACP, US Chamber of Commerce, NRA, AARP, AFL-CIO, AMA. View more lessons or practice this subject at https://www.khanacademy.org/humanities/ap-us-government-and-politics/political-participation/groups-influencing-policymaking/v/interest-groups-and-lobbying?utm_source=youtube&utm_medium=desc&utm_campaign=usgovernmentandcivics 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=-rr81Uf10pc Note: All Khan Academy content is available for free at (www.khanacademy.org)