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Browse High School Linear Algebra
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Vector questions.
 Definition of a Vector [02/28/2002]

I would like a "proper" definition of a vector and how concepts of
"magnitude" and "direction" arise in the discussion of vectors.
 Questions about Matrices [2/24/1995]

What is the inverse of a matrix, and how do you find it? How do you
multiply two matrices together?
 What is a Vector? [01/04/2002]

I am having trouble understanding exactly what a vector is and cannot
seem to find a simple, straightforward explanation.
 What is Linear Algebra? [09/06/1997]

I have absolutely no idea about linear algebra...
 3D Figures and Intersections [03/04/1999]

Determining whether a line and plane intersect, and where, using vectors.
 3D Geometry [11/17/1997]

You can draw a line of minimum distance between and perpendicular to two
lines in 3space. I know how to get the distance and direction of this
line, but I want to locate the line in 3space so that I can find its
midpoint.
 3D Points to a 2D computer screen [07/25/1997]

I am trying to write a 3D graphics engine that takes 8 points with their
own (X,Y,Z) coordinates to plot a CUBE in 3D space...
 An Absorbing States Problem [11/28/2000]

A mouse is in one of 4 rooms. If it finds cheese in the current room, it
stays there; if not, it exits to another room at random. What is the
probability it will get trapped? Are there any absorbing states?
 Adding Angles [03/27/2002]

I want to be able to add two angles without using sines or cosines,
because they aren't fast enough for programming games.
 The Adjoint of a Matrix [10/21/1998]

Given the adjoint of matrix A, how would you determine matrix A?
 Angle Between Vectors [06/07/2002]

Given vectors A and B in a plane, and vector C normal to that plane,
compute the clockwise angle from vector A to vector B when viewed in
the direction of the normal vector C.
 Ball Bouncing off a Line Segment [05/04/2001]

If you take an arbitrary line on a 2D plane, e.g. x1y1  x2y2, then take
a point that moves about the plane, say pxpy, can you tell if this point
has crossed the line at any time?
 Basis for a Vector Space in R^3 [11/25/1998]

Are the following bases for R^3: {(2,3,1), (4,1,1), (0,7,1)} ... ?
 BigO Notation in Matrix Multiplication [12/10/2000]

How can I prove that two n x n matrices can be multiplied in O(n^3) time?
Also, is there a faster way to multiply them?
 Calculating Angles Between Faces of a Solid [09/15/2003]

How can I compute the dihedral angles for a Great Rhombicosidodecahedron?
 Calculating Matrix Determinants by Expansion of Minors [11/19/2003]

When I calculate the determinant by expansion of minors in a 3 x 3
matrix, I always find that the result for the second row is the
opposite of the result for rows 1 and 3, and I don't understand why.
Can you explain it?
 Coin Tosses, Dealing Cards... [12/08/1998]

Several questions on discrete math  probability and combination;
deducing recurrence relations.
 Coordinates of Endpoint of a Segment [11/01/2002]

Determine the coordinates of the other endpoint of a segment with an
endpoint at (1,1) and a midpoint at (2,5).
 Cramer's Rule and a System of Two Equations [12/27/2003]

I have a system of two equations and two variables, 2x  6y = 12 and
4x + 3y = 7. How do I use Cramer's Rule to solve the system?
 Cramer's Rule in Action [05/08/1998]

Explaining Cramer's Rule by applying it to a system of equations.
 Crossed up by Scalars and Vectors [02/14/2012]

A student wonders why a dot product results in a scalar, whereas a cross product
produces a vector. Doctor Jerry introduces example vectors, their angles, and their
perpendiculars to illustrate how these operations arise.
 Cross Products; Rotating in Three Dimensions [10/26/2001]

Our class understands how the cross product works, but not why or the
proof behind it.
 Definition of an Identity Matrix [08/09/1999]

Which of the following would be an identity matrix?
 Definition of an Ntuple [09/20/1999]

What is an ntuple?
 Describing Eigenvalues and Eigenvectors [04/05/1998]

What is an eigenvalue? an eigenvector? What are some applications?
 Determinant of a Matrix [11/05/1997]

Can you give us a definition for the determinant of a matrix?
 Determinant of an Invertible Matrix [08/04/1999]

Could you explain and give a proof for why a matrix is invertible if and
only if the determinant is nonzero?
 Determinants and the Area of a Triangle [12/14/1998]

Given a triangle with vertices (A,B), (C,D), and (E,F), how do you find
the area in determinant form?
 Determinants of 4x4 Matrices [12/18/1996]

How do you find the determinant of a 4 x 4 matrix?
 Determining If A Polygon's Edges Cross [10/29/2003]

Is there a way to determine if a polygon has edges that cross by using
the coordinates of the vertices that define the polygon [(x1,y1) to
(xn,yn)]?
 Diagonalization of a Matrix [12/10/1998]

Diagonalize a 3x3 real matrix A (find P, D, and P^(1) so that A = P D
P^(1)).
 Distance Between 2 Lines: Vectors [8/19/1996]

What is the shortest distance between 2 lines?
 Distance Between a Line and a Point Using Vectors [09/25/1999]

How do you use scalar vector projections to prove that the distance
between the line ax+by+c = 0 and point (x1,y1) is
ax1+by1+c/sqrt(a^2+b^2)?
 Eigenvalues [12/18/1998]

What is an eigenvalue and how is it used?
 Equation for Angle Formed by Two Vectors [05/31/2000]

Do I need to find the vector equation of OP and OQ, or of PO and OQ, when
finding the angle POQ using the formula cos(theta)=a.b/ab?
 Equation of a Line in Three or More Dimensions [05/18/2000]

Can the equation y = mx + b be used to define a line in three dimensions?
What about four or more dimensions?
 Expansion by Minors [10/26/1999]

How do you evaluate the determinant of a 3x3 matrix using expansion by
minors?
 Explaining the Determinant [11/16/1997]

I am trying to understand what the determinant of a matrix actually is.
 Explaining the Dot Product [04/05/1998]

Exactly what does the dot product represent?
 Explanation of General Solution to Difference Equations [02/08/2006]

I know that the general solution to a difference equation like y(n) =
Ay(n1) + By(n2) is given by y(n) = as^n + bs^n when y is in the form
s^t. But I don't really know why that's the case. Can you explain
where that comes from?
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