- Null Matrix is a matrix having zero as each of its elements.
- Examples of zero matrix or null matrix
- The null matrix is also called a zero matrix.
- It can have different numbers of rows and columns.
- The addition of a null matrix to any matrix results in the same matrix.
- Null matrix is also called the additive identity of the given matrix.
- The order of a null matrix is m x n and it can have an unequal number of rows and columns.
- The addition of a zero matrix to any other matrix of the same order does not change the matrix and hence the null matrix is also called the additive identity.
Properties Of Zero Matrix (Null Matrix)
The following are some of the important properties of the null matrix.
- The null matrix can be a square matrix.
- The null matrix can have an unequal number of rows and columns.
- The multiplication of a null matrix with any other matrix changes the matrix into a null matrix.
- The determinant of a null matrix is equal to zero.
- Null matrix is a singular matrix |A|= O
Other matrices types
Order of a row matrix: A row matrix has one row and numerous columns. The order of the row matrix is 1 x n
Order of a column matrix: A column matrix has one column and numerous rows. The order of the column matrix is n x 1
Order of a square matrix: A square matrix has an equal number of rows and columns. The order of a square matrix is of the form n x n; where m=n
Application of matrices in Maths
- The matrices play a major role in Maths, as well as in engineering.
- It helps in solving linear equations.
- In cryptography, matrices are used to encrypt the data so it can be read by an individual.
- In wireless communication, matrixes are used to detect, extract, and evaluate the information encoded in signals.
- In computer science, matrices are used to represent linear transformations.
- In graphics, matrices are used to project three-dimensional images into two-dimensional planes. A digital image is represented as a matrix in graphics. The matrix’s rows and columns correspond to the rows and columns of pixels.
- Color values for a specific point of reference can be represented in pixels, and the numerical values correspond to the color of the pixels.
- In video games, changing or transforming a point (a character or any object) with matrices is a mathematical application.
- Bar graphs and line graphs are also expressed using values in matrices.
- In addition to this, matrices are used in Fourier analysis, Gauss theorem, and finding electric currents.
Questions to review your concepts:
What is a Null matrix?
What can be the possible order of a null matrix?
What is the additive identity matrix?
How do you multiply a matrix with a null matrix?
What are different types of matrices?
What is a singular matrix?
What is the determinant of a null matrix?
What are the applications of matrices in Math?
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