Example: This matrix is 2×3 (2 rows by 3 columns): When we do multiplication: The number of columns of the 1st matrix must equal the number of rows of the 2nd matrix .

We call the constant a scalar, so officially this is called "scalar multiplication". Multiplying by Another Matrix To multiply two matrices together is a bit more difficult ... read Multiplying …

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 …

To find the inverse of a 2x2 matrix: swap the positions of a and d, put negatives in front of b and c, and divide everything by the determinant (ad-bc). Sometimes there is no inverse at all 106, …

It also shows us why the order of multiplying matrices is important (unlike ordinary numbers which can be mulitiplied in any order, example 2×3=3×2). Transforms In Code. Need to code this …

Example: 6×7 + 2×7 + 3×7 + 5×7 + 4×7. 6×7 + 2×7 + 3×7 + 5×7 + 4×7 = (6+2+3+5+4) × 7 = 20 × 7 = 140

Here are some of the most common types of matrix: Square. A square matrix has the same number of rows as columns. A square matrix (2 rows, 2 columns) Also a square matrix (3 …

Example: Calculate the dot product of vectors a and b: a · b = |a| × |b| × cos(θ)

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 …

A matrix is an array of numbers (one or more rows, one or more columns). In fact a vector is also a matrix! Because a matrix can have just one row or one column. So the rules that work for …