Check whether the matrix
is invertible or not.
Step 1: Calculate the Determinant
For a \( 2 \times 2 \) matrix A =
, the determinant is given by: \[ \det(A) = (a d - b c). \] Substituting the values from matrix \( A \): \[ \det(A) = (\cos\theta \cdot \cos\theta - \sin\theta \cdot (-\sin\theta)) \] \[ = \cos^2\theta + \sin^2\theta. \] Step 2: Check the Invertibility Condition
Since \( \cos^2\theta + \sin^2\theta = 1 \), we have: \[ \det(A) = 1 \neq 0. \] As the determinant is nonzero, the matrix is invertible.
Complete the chain and rewrite in your answer paper \[ \begin{array}{|c|l|l|l|} \hline \textbf{No.} & \textbf{A} & \textbf{B} & \textbf{C} \\ \hline (1) & \text{Amazon River basin} & \text{Dense equatorial forest} & \text{Low population density} \\ \hline (2) & \text{Constructive Pyramid} & \text{More old age Population} & \text{Low birth rate and least death rate} \\ \hline (3) & \text{Industrial Region} & \text{Manufacturing Activities} & \text{Availability of Employment} \\ \hline (4) & \text{Pampas Grassland} & \text{Commercial cattle rearing} & \text{South America} \\ \hline (5) & \text{Private} & \text{Individual} & \text{Tata Iron and Steel Industries} \\ \hline \end{array} \]
Read the following passage and answer the questions given below:
Considering the latitudinal distribution of animal husbandry in the world, it is located between 30°N to 60°N and 30°S to 55°S latitudes.
Climate is one of the most influencing factors in the development of animal husbandry. It is more developed in the Northern Hemisphere. Presence of grasslands in Australia and North and South America has led to the distribution of this occupation. But, this occupation is influenced by advanced technology, market, and availability of large estates.
It has developed on a commercial basis in North America, South America, and Australia. The animal husbandry in North and South America is carried out with the help of advanced technology on a commercial scale.
Dense forests, inhospitable climate, low-quality fodder in the equatorial region has discouraged the development of animal husbandry in these regions.