Are you curious to know what is null matrix? You have come to the right place as I am going to tell you everything about null matrix in a very simple explanation. Without further discussion let’s begin to know what is null matrix?
In linear algebra, a null matrix is a matrix consisting of all zero entries. In this blog post, we will explore what a null matrix is, how it is represented, and its properties in linear algebra.
What Is Null Matrix?
A null matrix, also known as a zero matrix, is a matrix in which every entry is zero. A null matrix can be of any size, from a 1×1 matrix to an nxn matrix.
A null matrix is denoted by the symbol 0, and it is important to note that the null matrix is different from the identity matrix, which is a square matrix with diagonal entries equal to 1 and all other entries equal to 0.
Representation Of Null Matrix:
A null matrix is represented by a rectangular array of numbers with all entries equal to 0. For example, a 3×3 null matrix can be represented as:
[0 0 0]
[0 0 0]
[0 0 0]
Properties Of Null Matrix:
- Addition: When a null matrix is added to any matrix, the resulting matrix is the same as the original matrix. That is A + 0 = A for any matrix A.
- Multiplication: When a null matrix is multiplied by any matrix, the resulting matrix is also a null matrix. That is A x 0 = 0 for any matrix A.
- Rank: The rank of a null matrix is always zero. This is because the rows and columns of a null matrix are linearly dependent, and any row or column can be expressed as a linear combination of the other rows or columns.
- Inverse: A null matrix does not have an inverse because it is not possible to find a matrix that, when multiplied by the null matrix, results in the identity matrix.
Conclusion:
In conclusion, a null matrix is a matrix consisting of all zero entries. It is represented by the symbol 0 and has several important properties, including its role in addition and multiplication, its rank, and the fact that it does not have an inverse. In linear algebra, the null matrix is a fundamental concept that is essential to understanding the properties and operations of matrices.
FAQ
What Is Meant By Null Matrix?
A zero matrix is a matrix that has all its elements equal to zero. Since a zero matrix contains only zeros as its elements, therefore, it is also called a null matrix.
What Is A Null Matrix With An Example?
The matrix whose every element is zero is called a null or zero matrices and it is denoted by 0. For example, [00] is a zero matrix of order 1 × 2. [00] is a zero or null matrix of order 2 × 1.
Is The Null Matrix A Diagonal?
- A null (zero) matrix is a matrix in which all elements are zero. 5. A diagonal matrix is a matrix in which all of the elements not on the diagonal of a square matrix are 0.
What Is Called Null?
Null means having no value; in other words null is zero, like if you put so little sugar in your coffee that it’s practically null. Null also means invalid, or having no binding force. From the Latin nullus, meaning “not any,” poor, powerless null is not actually there at all.
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