Mathematics 10 — Exercise 3.3 · Q2 (i)

Full question

Find X + Y.

Step-by-step solution

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

   $$(\left[\begin{array}{cc}1& -1\\ -2& 2\end{array}\right],\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right])$$

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

   $$1+1=2$$

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

   $$-1+2=1$$

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

   $$-2+3=1$$

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

   $$2+4=6$$

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

   $$\left[\begin{array}{cc}2& 1\\ 1& 6\end{array}\right]$$

Answer

The final answer is shown below.