JAMB Mathematics Past Questions & Answers - Page 322

Since there are 5 angles given, the polygon is a pentagon.

Sum of interior angles of a pentagon = (2(5) - 4) x 90° = 540°

\(\therefore\) x + 2x + 3x + 4x + 5x = 15x

15x = 540°

\(x = \frac{540}{15} = 36°\)

Recall that a unit matrice is a diagonal matrix in which the elements in the leading diagonal is unity. Therefore,

I₃ = \(\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}\)

I₃ = \(+1\begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix} - 0\begin{vmatrix} 0 & 0 \\ 0 & 1 \end{vmatrix} + 0 \begin{vmatrix} 0 & 1 \\ 0 & 0 \end{vmatrix} \)

I₃ = +1(1 - 0) - 0(0 - 0) + 0(0 - 0)

= 1(1)

= 1

\(\begin{vmatrix} 5 & 3 \\ x & 2 \end{vmatrix}\) = \(\begin{vmatrix} 3 & 5 \\ 4 & 5 \end{vmatrix}\)

10 - 3x = 15 - 20

-3x = 15 - 20 - 10

-3x = -15

x = 5

m * n = \(\frac{mn}{2}\)

Identify, e = 2

Let a \(\in\) R, then

a * a\(^{-1}\) = e

a * a\(^{-1}\) = 2

-5 * a\(^{-1}\) = 2

\(\frac{-5 \times a^{-1}}{2} = 2\)

\(a^{-1} = \frac{2 \times 2}{-5}\)

\(a^{-1} = -\frac{4}{5}\)

p * q = pq + p - q First execute for 3 * 4 ==> 3(4) + 3 - 4 = 12 + 3 - 4 = 11 Now we execute for 2 * 11 ==> 2(11) + 2 - 11 = 22 + 2 - 11 = 13