Mathematics 10 — Exercise 3.3 · Q2 (iii)

Full question

Find 4X − Z.

Step-by-step solution

1. Multiply every matrix entry by the scalar.

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

2. Entry (1,1): multiply its value by the scalar.

   $$4\times 1=4$$

3. Entry (1,2): multiply its value by the scalar.

   $$4\times \left(-1\right)=-4$$

4. Entry (2,1): multiply its value by the scalar.

   $$4\times \left(-2\right)=-8$$

5. Entry (2,2): multiply its value by the scalar.

   $$4\times 2=8$$

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

   $$\left[\begin{array}{cc}4& -4\\ -8& 8\end{array}\right]$$

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

   $$(\left[\begin{array}{cc}4& -4\\ -8& 8\end{array}\right],\left[\begin{array}{cc}3& 0\\ 0& -2\end{array}\right])$$

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

   $$4-3=1$$

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

   $$-4+0=-4$$

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

    $$-8+0=-8$$

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

    $$8+2=10$$

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

    $$\left[\begin{array}{cc}1& -4\\ -8& 10\end{array}\right]$$

Answer

The final answer is shown below.