Mathematics 10 — Exercise 3.3 · Q2 (vi)

Full question

Find Z − Z.

Step-by-step solution

1. The orders match. Combine only entries in the same row and column.

   $$(\left[\begin{array}{cc}3& 0\\ 0& -2\end{array}\right],\left[\begin{array}{cc}3& 0\\ 0& -2\end{array}\right])$$

2. Entry (1,1): subtract the corresponding entries.

   $$3-3=0$$

3. Entry (1,2): subtract the corresponding entries.

   $$0+0=0$$

4. Entry (2,1): subtract the corresponding entries.

   $$0+0=0$$

5. Entry (2,2): subtract the corresponding entries.

   $$-2+2=0$$

6. Place the calculated entries in their original row and column positions.

   $$\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$$

Answer

The final answer is shown below.