Question

If a matrix has
n^2 entries, where n ∈ N , then it is a square matrix. Is it true or false? Justify your answer.

Answer 1

Answer on Question #78423 – Math – Linear Algebra

Question

If a matrix has $n^2$ entries, where $n \in \mathbb{N}$, then it is a square matrix. Is it true or false? Justify your answer.

Solution

False. The number of entries is equal to the number of columns $(c)$ multiplied by the number of rows $(r)$:

$$N = c * r$$

Let $N = n^2 = c * r$.

For example, if $c = 2, r = 8 \rightarrow N = 16 = 4^2$

and the matrix is not a square matrix.

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