`[B] = k*[(A_(11), A_(12)), (A_(21), A_(22))]`

Enter a value for all fields

The Multiplication of a 2x2 Matrix by a Scalar calculator computes the resulting 2x2 matrix (B) produced by the scalar multiplication of 2x2 matrix A and scalar k.

INSTRUCTIONS:  Enter the following:

• (A)  2x2 matrix
• (k) scalar

2x2 matrix (B): The calculator will compute the two rows of the resulting 2x2 matrix (B)

2x2 Matrix Calculators :

• To compute the Characteristic Polynomial of a 3x3 matrix,CLICK HERE.
• To compute the Trace of a 2x2 Matrix, CLICK HERE.
• To compute the Determinant of a 2x2 Matrix, CLICK HERE.
• To compute the Inverse of a 2x2 Matrix, CLICK HERE.
• To compute the Eigenvalues of a 2x2 Matrix, CLICK HERE.
• For the Classifying Equilibria of a 2x2 Matrix, CLICK HERE.
• To compute the Eigenvalues and Eigenvectors of a 2x2 Matrix, CLICK HERE.
• To compute the Characteristic Polynomial of a 2x2 Matrix, CLICK HERE.

Introduction

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). 

Sources

Williams, Gareth. Linear Algebra With Applications. Boston: Jones and Bartlett, 2011. Print.