NECO 2023 · Paper 2 · Q9

(a)
Given $A = \begin{pmatrix} 3 & 2 & -1 \\ 1 & 0 & 1 \\ 2 & -2 & 0 \end{pmatrix}$ and $B = \begin{pmatrix} 4 & 2 & -3 \\ 3 & -1 & 1 \\ 0 & -2 & 2 \end{pmatrix}$ , evaluate (i) $3A - 2B$ ; (ii) $|3A - 2B|$ .
(b)
Mr. Tony took a loan of ₦120,000.00 at $12\%$ per annum compound interest to buy a piece of land. (i) If he paid the loan in three years, what was the total amount paid? (ii) Find his profit if he later sold the land for ₦350,000.00 without any additional expenses.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Multiply each matrix by its number, then subtract entry by entry: $3A - 2B = \begin{pmatrix} 9 - 8 & 6 - 4 & -3 + 6 \\ 3 - 6 & 0 + 2 & 3 - 2 \\ 6 - 0 & -6 + 4 & 0 - 4 \end{pmatrix}$
$= \begin{pmatrix} 1 & 2 & 3 \\ -3 & 2 & 1 \\ 6 & -2 & -4 \end{pmatrix}$ .

Expand along the first row: $1\big(2(-4) - 1(-2)\big) - 2\big((-3)(-4) - 1(6)\big) + 3\big((-3)(-2) - 2(6)\big) = 1(-6) - 2(6) + 3(-6)$
$= -36$ .

Compound interest at $12\%$ for 3 years: $120\,000 \times 1.12^3 = 120\,000 \times 1.404928$
$= ₦168,591.36$ .