Question

Which statement correctly compares \[\begin{bmatrix}1&2\\3&4\end{bmatrix}\] and \[\begin{bmatrix}1&3\\2&4\end{bmatrix}\]?

Options

• The matrices are equal because they contain the same numbers.

• \[\begin{bmatrix}1&2\\3&4\end{bmatrix}\ne\begin{bmatrix}1&3\\2&4\end{bmatrix}\] because the same numbers occur in different positions.

• The matrices are equal because the entries \[1\] and \[4\] are in the same positions.

• The matrices are equal because both have order \[2\times2\].

Answer 1

Matrices containing the same numbers are not necessarily equal if the numbers occur in different positions. Here, the entries in positions \[(1,2)\] and \[(2,1)\] differ.