The Multiplication of a 3x3 Matrix by a Scalar calculator computes the resulting 3x3 matrix (B) produced by the scalar multiplication of 3x3 matrix A and scalar c.
INSTRUCTIONS:
- (A) 3x3 Matrix
- (c) scalar
Matrix (B): The calculator returns the resultant matrix.
The Math / Science
Matrices consist of rows and columns, where given a matrix `A`, the position in `A` in vCalc is denoted `A_(ij)` where the `1^(st)` subscript indicates the row of the matrix and the `2^(nd)` subscript indicates the column of the matrix. We refer to `A_(ij)` as the `(i, j)"th"` element of the matrix `A`. An arbitrary matrix has its size denoted as `mtimesn`, where `m` refers to the number of rows in a given matrix and `n` refers to the number of columns in a given matrix.
If `m=n` then the matrix is referred to as a square matrix. The elements of the matrix `A_(11), A_(22), ..., A_(text(nn))` is commonly referred to as the main diagonal of the square matrix.
Scalar Multiplication
Let `A` be a matrix and `c` be an arbitrary scalar number; scalar multiplication of `A` by `c` is "the matrix obtained by multiplying every element of `A` by `c`. The matrix `cA` will be the same size as `A`" (Williams, 37).
Matrix Calculators
- Determinant of 3-by-3 Matrix
- Characteristic Polynomial of a 3x3 matrix
- Inverse of a 3x3 Matrix
- Transpose of a 3x3 Matrix
- Trace of a 3x3 Matrix
- Mirror of a 3x3 Matrix
- 3x3 Matrix Characteristics (Trace, Determinant, Inverse, Characteristic Polynomial)
- Product of a 3x3 matrix and a Scalar
- Product of a 3x3 matrix and a 3x1 matrix
- Product of two 3x3 matrices
- Solving 3 Equations with 3 Unknowns
- Cramer's Rule (three equations, solved for x, y and z)
- Cramer's Rule Calculator
Sources
Williams, Gareth. Linear Algebra With Applications. Boston: Jones and Bartlett, 2011. Print.