The angles of a polygon are given by x, 2x, 3x, 4x and 5x respectively. Find the value of x.
24o
30o
33o
36o
Correct answer is D
Since there are 5 angles given, the polygon is a pentagon.
Sum of interior angles of a pentagon = (2(5) - 4) x 90° = 540°
∴ x + 2x + 3x + 4x + 5x = 15x
15x = 540°
x = \frac{540}{15} = 36°
Given that I3 is a unit matrix of order 3, find |I3|
-1
0
1
2
Correct answer is C
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
3
4
5
7
Correct answer is C
\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
-\frac{4}{5}
-\frac{2}{5}
4
5
Correct answer is A
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}