Question

Given \[P=\begin{bmatrix}1&2\\3&4\end{bmatrix}\] and \[Q=\begin{bmatrix}1&2\\3&5\end{bmatrix}\], why is \[P\ne Q\]?

Options

• The matrices have different order.

• The element in position \[(1,1)\] is different.

• Both matrices have order \[2\times2\], but the element in position \[(2,2)\] is different: \[4\ne5\].

• The element in position \[(1,2)\] is different.

Answer 1

Both \[P\] and \[Q\] have order \[2\times2\], so their corresponding elements can be compared. Their entries in position \[(2,2)\] are \[4\] and \[5\], which are not equal.