How to Multiply Matrices - Math is Fun
To multiply an m×n matrix by an n×p matrix, the n s must be the same, and the result is an m×p matrix. So ... multiplying a 1×3 by a 3×1 gets a 1×1 result:
Matrices - Math is Fun
So we don't divide, instead we multiply by an inverse. And there are special ways to find the Inverse, learn more at Inverse of a Matrix. Transposing. To "transpose" a matrix, swap the rows and columns. We put a "T" in the top right-hand corner to mean transpose:
Matrix Calculator - Math is Fun
Enter your matrix in the cells below A or B. ... Or you can type in the big output area and press to A or to B (the calculator will try its best to interpret your data).
Algebra 2 - Math is Fun
Multiplying Complex Numbers; The Complex Plane; Common Number Sets; Inequalities "Equal To" is nice but not always available. Maybe we only know that something is less than, or greater than. So let's learn about inequalities. a≥b. Introduction to Inequalities; Properties of Inequalities; Solving Inequalities; Solving Inequality Word Questions ...
Inverse of a Matrix - Math is Fun
When we multiply a matrix by its inverse we get the Identity Matrix (which is like "1" for matrices):
Dot Product - Math is Fun
So we multiply the length of a times the length of b, then multiply by the cosine of the angle between a and b OR we can calculate it this way: a · b = a x × b x + a y × b y
Transformations and Matrices - Math is Fun
Matrices can also do 3D transformations, transform from 3D to 2D (very useful for computer graphics), and much much more. The Mathematics. For each [x,y] point that makes up the shape we do this matrix multiplication:
Determinant of a Matrix - Math is Fun
To work out the determinant of a 3×3 matrix: Multiply a by the determinant of the 2×2 matrix that is not in a's row or column. Likewise for b, and for c; Sum them up, but remember the minus in front of the b; As a formula (remember the vertical bars || mean "determinant of"): "The determinant of A equals a times the determinant of ... etc"
Scalar, Vector, Matrix - Math is Fun
How do we multiply two vectors together? There is more than one way! The scalar or Dot Product (the result is a scalar). The vector or Cross Product (the result is a vector). (Read those pages for more details.)
Solving Systems of Linear Equations Using Matrices - Math is Fun
A is the 3x3 matrix of x, y and z coefficients; X is x, y and z, and; B is 6, −4 and 27; Then (as shown on the Inverse of a Matrix page) the solution is this: X = A-1 B. What does that mean? It means that we can find the X matrix (the values of x, y and z) by multiplying the inverse of the A matrix by the B matrix. So let's go ahead and do that.