Equality of Matrices

==2024-12-03

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Theory

Two matrices A = $[a_{ij}{]}_{m_a\times n_a}$, B = $[b_{ij}{]}_{m_b\times n_b}$ are said to be equal in following condition: $A=B⟺(m_a=m_b\Lambda n_a=n_b)\Lambda (a_{ij}=b_{ij})$

Examples

Given,

$$A=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\end{array}\right]$$ $$B=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\end{array}\right]$$

Then, $A=B$.

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Given,

$$A=\left[\begin{array}{ccc}9& 7& 5\\ 1& 9& 8\end{array}\right]$$ $$B=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\end{array}\right]$$

Then $A\ne B$ because corresponding elements aren’t equal.

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Given,

$$A=\left[\begin{array}{ccc}9& 7& 5\\ 1& 9& 8\end{array}\right]$$ $$B=\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$$

Then $A\ne B$ because order of the matrices aren’t equal.

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PTR