6th October 2019

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# What is the rank of a matrix?

The maximum number of linearly independent vectors in a matrix is equal to the number of non-zero rows in its row echelon matrix. Therefore, to find the rank of a matrix, we simply transform the matrix to its row echelon form and count the number of non-zero rows.

Similarly, you may ask, when a matrix is invertible?

If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A1. A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0.

How do you know if the inverse of a matrix exists?

If the determinant of the matrix is zero, then it will not have an inverse; the matrix is then said to be singular. Only non-singular matrices have inverses. Find the inverse of the matrix A = ( 3 1 4 2 ). result should be the identity matrix I = ( 1 0 0 1 ).

Is an all zero matrix invertible?

square matrix is not invertible if at least one row or column is zero.