Question

if rank of unit matrix of order 4 is----
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Answer 1

Answer:

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Answer 2

Rank of an unit matrix of order 4 is 4

Given :

An unit matrix of order 4

To find :

Rank of the unit matrix of order 4

Concept :

Rank of a matrix :

Let A be a non zero matrix of order m × n. The Rank of A is defined to be the greatest positive integer r such that A has at least one non-zero minor of order r

For a non-zero m × n matrix A

0 < rank of A ≤ min {m, n}

For a non-zero matrix A of order n,

rank of A < , or = n according as A is singular or non-singular

Solution :

Step 1 of 2 :

Write down the given matrix

Let A be the given matrix

Then A is unit matrix of order 4

$\displaystyle \sf A = \begin{pmatrix} 1 & 0 & 0&0\\ 0 & 1 & 0&0 \\ 0 & 0 & 1 &0\\ 0 & 0 & 0&1\end{pmatrix}$

Step 2 of 2 :

Find rank of the matrix

Since A is the unit matrix of order 4

So A is a non singular matrix

So rank of the matrix = 4

∴ Rank of an unit matrix of order 4 is 4

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