Transforming vectors using matrices Opens a modal. Transforming polygons using matrices Opens a modal. Matrices as transformations Opens a modal. Matrix from visual representation of transformation Opens a modal. Visual representation of transformation from matrix Opens a modal. Use matrices to transform 3D and 4D vectors.
Transform polygons using matrices. Understand matrices as transformations of the plane. Determinant of a 2x2 matrix. Determinant of a 2x2 matrix Opens a modal. Introduction to matrix inverses. Intro to matrix inverses Opens a modal. Determining invertible matrices Opens a modal. Determine inverse matrices. Determine invertible matrices. Finding the inverse of a matrix using its determinant.
Finding inverses of 2x2 matrices Opens a modal. Practice finding the inverses of 2x2 matrices. Learn No videos or articles available in this lesson.
Find the inverse of a 2x2 matrix. Determinant of a 3x3 matrix: standard method 1 of 2 Opens a modal. Determinant of a 3x3 matrix: shortcut method 2 of 2 Opens a modal.
Inverting a 3x3 matrix using Gaussian elimination Opens a modal. Inverting a 3x3 matrix using determinants Part 1: Matrix of minors and cofactor matrix Opens a modal. We proceed along the first row and multiply each component by the determinant of the submatrix formed by ignoring that component's row and column. Each of these terms is added together, only with alternating signs i.
But I'd rather use my brain's synaptic connections to do something more useful. In fact, I'm afraid if I tried to memorize it, I might forget something else important, like how to combine like terms in algebra. The above procedure generalizes to larger determinants. That's too messy to write down. But if you had to, you could do it. For large systems of equations, we use a computer to find the solution.
This chapter first shows you the basics of matrix arithmetic, and then we show some computer examples using Scientific Notebook or similar so that you understand what the computer is doing for you. You can skip over the next part if you want to go straight to matrices. A determinant of a matrix represents a single number.
We obtain this value by multiplying and adding its elements in a special way. We can use the determinant of a matrix to solve a system of simultaneous equations. We'll see in the next section how to evaluate this determinant. It has value Determinants - derived from a square matrix, a determinant needs to be multiplied out to give a single number.
Large Determinants - this section will help you to understand smaller determinants. Multiplication of Matrices - how to multiply matrices of different sizes. Includes an interactive where you can explore the concept. Finding the Inverse of a Matrix - which we use to solve systems of equations.
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