Multiplication of a 3x3 Matrix by a Scalar

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.