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 TOPICS This page:   linear algebra    Search   Dr. Math See also the Internet Library:   linear algebra HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Linear Algebra Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Vector questions. Matrices and Computer Programming [11/05/1996] Why are matrix multiplication and matrix algebra the way they are? Matrices and TI Calculators [03/06/1997] How do I solve a set of three equations in three unknowns using matrices on my TI-82 calculator? Matrix Algebra [06/01/1998] Solving for X in the matrix product A*X - X*B = C. Matrix Division? [06/26/2006] Is it possible to divide matrices? Matrix Encoder and Decoder [07/22/2003] How does the decoder work? Matrix Inverses [04/07/1998] Can you find a 2x2 matrix A such that A^2 = I? Can you find a 2x2 matrix that has no inverse? Matrix Multiplication [09/04/1997] I am doing a project in Algebra 2 and must research matrix multiplication. Matrix Multiplication [12/18/1998] Why does matrix multiplication work? Why are the rows multiplied and added with the columns? Matrix Multiplication [10/11/2003] I'm trying to multiply two matrices. I know what the dimensions of the product have to be, but how do I do the actual multiplication? Matrix Questions: Addition, Inverse [8/6/1996] (1 2) + (-1 -2) =? and if A = (3 4), does A inverse exist? Matrix Rank [09/29/2001] I want to find the rank of a matrix, but I don't know how to compute rank. Matrix: Why Use m and n? [09/06/2001] Why do we use m and n, with x between them, to represent order in a matrix? Matrix with No Inverse [06/13/2005] Are there are 3x3 matrices that do not have inverses? If so, can you give me an example? Maximum Difference, Longitude and Latitude [04/10/2001] Find the maximum longitude and latitude difference between two points on Earth 1000 kilometers apart. Minimum Matrix Multiplication [02/16/2003] Find a way to multiply n matrices using a minimum number of multiplications of the entities. More on the Intersection of Two Lines in Three Dimensions [02/17/2009] How to isolate for "a" in the vector equation a(V1 x V2) = (P2 - P1) x V2, with a suggestion for computer coding. Multiplicative Inverse in Finite Field GF(2^8) [02/23/2005] Is the multiplicative inverse of a 4x4 matrix in GF(2^8) the same as the inverse of any 4x4 matrix? Multiplying a Matrix By a Scalar [08/27/1998] When you multiply a scaler times a matrix, the result is a new matrix... Multiplying Matrices and Identifying Dimensionality [07/16/2003] I understand adding and subtracting matrices, but not multiplying them. Also, how can I find the dimensionality of the following matrix...? Natural Numbers Coprime to 6 [02/16/1998] Let N(x) denote the number of natural numbers less than x which are coprime to 6. Show that lim as x goes to infinity of [N(x)/x] = 1/3. Nearest Point on a Great Circle [05/27/2002] Given points A, B, and C on the surface of a unit sphere, find the point P on the great circle defined by A and B that is nearest to C. Pane Rotation - Computer Graphics [11/14/1996] How do I find a formula for rotating a pane in space? Parallelepipeds [05/06/1997] What is the formula for finding the total surface area of a parallelepiped? Parametrics [12/18/1996] You're in 3-D space at point A, you want to get to point B, and you know the coordinates to point B from point C (but B is moving). What heading do you need to set in order to meet point B? Point Inside or Outside Triangle? [08/02/2001] I have coordinates of three vertices of the triangle and coordinates of the point. Point within a Triangle [05/29/2003] I have the coordinates of the three corners of a equilateral triangle ABC. How can I decide whether an arbitrary point (X,Y) lies in the plane of the triangle? Powers of Matrices [6/27/1996] Would you send me some information/links about matrices and exponentials? Principal Axis Theorem [12/10/1997] Could you give me applications of the principal axis theorem? Product of Upper Triangular Matrices [09/23/2003] Show that the product of two upper triangular matrices is an upper triangular matrix. Proof About Matrices [06/02/1999] How do I prove that in two 2 x 2 matrices, A and B, AB - BA will never be the multiplication identity matrix? Properties of Determinants [10/23/2000] What properties of determinants do we use to evaluate them, and how? How do we put determinants in row-echelon form? Prove Choice of Scalars Unique [03/13/2001] Suppose B = {v1,v2, ... vn} is a basis for a vector space V. Let u element of V be any vector. Prove that the expression of u in terms of the basis B is unique. Raytrace of a Star Sapphire [12/11/1996] How do I find the rotations necessary to create a raytrace of a star sapphire so that the star always faces the camera? Rearranging Matrices [11/5/1995] My problem involves matrices, specifically 9x9 size. I would like to know how to determine what order to rearrange the rows so the numbers in the diagonal add up to the maximum possible value. Redundant Sets of Equations [02/07/1997] Is there a solution to the set consisting of these three equations: x + y + z = 50, 2x + 3y + 4z = 158, and 4x + 3y + 2z = 142? A Re-Framing Inversion: Transforming the Coordinates in Between [03/27/2012] Given some function that pass through (0, 0) and (1, 1), a student struggles to invert it after zooming in on two in-between points and re-centering on them as the new origin and (1, 1). Doctor Peterson obliges, starting with a sketch and simpler labels. Rotación de Véctores (3-D Vector Rotation) [6/19/1996] Hay alguna fórmula para rotar véctores en el espacio sobre los tres ejes de coordenadas? Rotating a cube in space [12/5/1994] I am a high school teacher, with a student interested in writing a program to show a cube on the screen and then rotate it by moving the corners around. He has asked me for equations. I don't have any. Do you? Rotating a Plane about a Point in Space [07/03/2004] Discussion of a method of rotating the three points of a right triangle around a point to align with a given plane in a particular way. Rotation Matrix about a Point Other Than the Origin [12/18/2006] I know that in order to rotate a point around the origin you use the rotation matrix with sine and cosine. I was wondering how you rotate a point around a point other than the origin? Page: []

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