Question

Which of the following statement are false? (A) the rank of the unit matrix of order n is unity . (B) the rank of null matrix is zero. (C) the rank of m×n matrix cannot exceed the minimum of m and n . (D) equivalent matrix have the same rank

Answer 1

Statement 1 is false

we know that the number of non zero rows in the reduced echelon form is the rank of the matrix.
Let us take an indentity matrix or unit matrix of order 3×3.
In our case non zero rows are 3 hence rank of matrix is ρ = 3.
In this way we can generalise our deduction and can say rank of unit matrix of order n is n.

Statement 2 is true

Statement 3 is true

Statement 4 is true