Mathematics Questions and Answers

Interior angle = (n - 2)180

but, n = 12

= (12 -2)180

= 10 x 180

= 1800

let each interior angle = x

x = \(\frac{(n - 2)180}{n}\)

x = \(\frac{1800}{12}\)

= 150^o

N = [2 3]

N^-1 = \(\frac{adj N}{|N|}\)

adj N = \(\begin{vmatrix} 4 & -3 \\ -1 & 2 \end{vmatrix}\)

|N| = (2 x4) - (1 x 3)

= 8 - 3

=5

N^-1 = \(\frac {1}{5}\) \(\begin{vmatrix} 4 & -3 \\ -1 & 2 \end{vmatrix}\)

\(\begin{vmatrix} 4 & 2 & -1 \\ 2 & 3 & -1 \\ -1 & 1 & 3 \end{vmatrix}\)

4 \(\begin{vmatrix} 3 & -1 \\ 1 & 3 \end{vmatrix}\) -2 \(\begin{vmatrix} 2 & -1 \\ -1 & 3\end{vmatrix}\) -1 \(\begin{vmatrix} 2 & 3 \\ -1 & 1 \end{vmatrix}\)

4[(3 x 3) - (-1 x 1)] -2 [(2x 3) - (-1 x -1)] -1 [(2 x 1) - (-1 x 3)]

= 4[9 + 1] -2 [6 - 1] -1 [2 + 3]

= 4(10) - 2(5) - 1(5)

= 40 - 10 - 5

= 25

\(\begin{vmatrix} 2 & 3 \\ 5 & 3x \end{vmatrix}\) = \(\begin{vmatrix} 4 & 1 \\ 3 & 2x \end{vmatrix}\)

(2 x 3x) - (5 x 3) = (4 x 2x) - (3 x 1)

6x - 15 = 8x - 3

6x - 8x = 15 - 3

-2x = 12

x = \(\frac{12}{-2}\)

= -6

N + Y = XY + X + Y

3 + -\(\frac{2}{3}\) = 3(- \(\frac{2}{3}\)) + 3 + (- \(\frac{2}{3}\))

= -2 + 3 -\(\frac{2}{3}\)

= \(\frac{1 - 2}{1 - 3}\)

= \(\frac{1}{3}\)