How to Multiply Matrices - Math is Fun
How to Multiply Matrices. A Matrix is an array of numbers: To multiply a matrix by a single number is easy: These are the calculations: We call the number ("2" in this case) a scalar, so this is called "scalar multiplication".
Matrices - Math is Fun
We can multiply a matrix by a constant (the value 2 in this case): These are the calculations: 2×4=8. 2×0=0. 2×1=2. 2×−9=−18. We call the constant a scalar, so officially this is called "scalar multiplication".
Determinant of a Matrix - Math is Fun
The determinant is a special number that can be calculated from a matrix. The matrix has to be square (same number of rows and columns) like this one: 3 8 4 6. A Matrix. (This one has 2 Rows and 2 Columns) Let us calculate the determinant of that matrix: 3×6 − 8×4. = 18 − 32.
Inverse of a Matrix - Math is Fun
Inverse of a Matrix. We write A-1 instead of 1 A because we don't divide by a matrix! And there are other similarities: When we multiply a number by its reciprocal we get 1: 8 × 1 8 = 1. When we multiply a matrix by its inverse we get the Identity Matrix (which is like "1" for matrices): A × A …
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).
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.
Dot Product - Math is Fun
We can calculate the Dot Product of two vectors this way: a · b = | a | × | b | × cos (θ) Where: | a | is the magnitude (length) of vector a. | b | is the magnitude (length) of vector b. θ is the angle between a and b.
Transformations and Matrices - Math is Fun
Transformations and Matrices. A matrix can do geometric transformations! Have a play with this 2D transformation app: Matrices can also do 3D transformations, transform from 3D to 2D (very useful for computer graphics), and much much more.
Commutative, Associative and Distributive Laws - Math is Fun
multiply a number by a group of numbers added together, or; do each multiply separately then add them
Eigenvector and Eigenvalue - Math is Fun
Notice how we multiply a matrix by a vector and get the same result as when we multiply a scalar (just a number) by that vector. How do we find these eigen things? We start by finding the eigenvalue .