**Category : **JEE Main & Advanced

A matrix *A* is said to be in Echelon form if either *A* is the null matrix or *A* satisfies the following conditions:

(1) Every non- zero row in *A* precedes every zero row.

(2) The number of zeros before the first non-zero element in a row is less than the number of such zeros in the next row.

If can be easily proved that the rank of a matrix in Echelon form is equal to the number of non-zero row of the matrix.

** **

**Rank of a matrix in Echelon form : **The rank of a matrix in Echelon form is equal to the number of non-zero rows in that matrix.

*play_arrow*Definition*play_arrow*Order of a Matrix*play_arrow*Equality of Matrices*play_arrow*Types of Matrices*play_arrow*Trace of a Matrix*play_arrow*Addition and Subtraction of Matrices*play_arrow*Scalar Multiplication of Matrices*play_arrow*Multiplication of Matrices*play_arrow*Positive Integral Powers of a Matrix*play_arrow*Transpose of a Matrix*play_arrow*Special Types of Matrices*play_arrow*Adjoint of a Square Matrix*play_arrow*Inverse of a Matrix*play_arrow*Rank of Matrix*play_arrow*Echelon Form of a Matrix*play_arrow*Homogeneous and Non-homogeneous Systems of Linear Equations*play_arrow*Consistency of a System of Linear Equation \[\mathbf{AX=B,}\] where \[\mathbf{A}\] is a square matrix*play_arrow*Cayley-Hamilton Theorem*play_arrow*Geometrical Transformations*play_arrow*Matrices of Rotation of Axes

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