What is a Zero Matrix?
A Zero Matrix is a matrix consisting of all zeroes. Also known as a "Null Matrix," the Zero Matrix acts similarly to the way the number zero operates with real numbers.
How does a Zero Matrix work?
Zero Matrices work in the same way that one may use the number zero in everyday operations. For example, a matrix of any values added by a zero matrix results in the initial matrix. Accordingly, a matrix of any values multiplied by the scalar 0, results in a zero matrix. Furthermore, a matrix of any values added to its opposite (i.e. 2 + -2) produces in a zero matrix.
Application of the Zero Matrix
Zero Matrices allow for simple solutions to algebraic equations involving matrices. For example, the zero matrix can be defined as an additive group, so in cases where one may need to solve for an unknown matrix, the zero matrix can be a valuable variable.
For example, imagine solving the equation X + Y = Z for X. First, using the additive inverse of the matrix Y, denoted -Y, simplify the equation to X + 0 = Z + (-Y). By adding the inverse matrix to either side of the equation, Y and -Y become a zero matrix. Then, using the additive identity property, X + 0 becomes just X, resulting in X = Z - Y. Through use of the zero matrix, algebraic equations are much easier to calculate.