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
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:
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"
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):
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
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
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).
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:
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 using Minors, Cofactors and Adjugate - Math is …
Note: also check out Matrix Inverse by Row Operations and the Matrix Calculator . We can calculate the Inverse of a Matrix by: Step 1: calculating the Matrix of Minors, Step 2: then turn that into the Matrix of Cofactors, Step 3: then the Adjugate, and; Step 4: multiply that by 1/Determinant. But it is best explained by working through an example!