Question

rank of 4×4 unit matrix
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Answer 1

Step-by-step explanation:

Rank of unit matrix [math]I_n[/math] of order n is n.

For example: Let us take an indentity matrix or unit matrix of order 3×3.

[math] I_3 [/math] = \begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}

We can see that it is an Echelon Form or triangular Form . Now we know that the number of non zero rows of the reduced echelon form is the rank of the matrix.

In our case non zero rows are 3 hence rank of matrix is [math]\rho[/math] = 3.

In this way we can generalise our deduction and can say rank of unit matrix of order n is n.