Given P = \(\begin{bmatrix}1 & 2\\2 & 3\end{bmatrix}\), find P\(^2\) - 4P - I where I is the identity matrix
If A = \(\begin{pmatrix}3 & 2 & 1\\4 & 2 & -1\end{pmatrix}\) and B = \(\begin{pmatrix}1 & 4\\0 & 1\\3 & 2\end{pmatrix}\). Find A\(^T\) + B, ( where T means transpose)
If tan\(\theta\) = \(\frac{8}{15}\), simplify \(\frac{ Sin\theta - Cos\theta}{Sin^2\theta - Sin\theta}\)
A binary operation * is defined on a set of real numbers by x*y = x\(^y\) for all values of x and y, if x * 2 = x, find the possible values of x.
The weights of 15 students in a class are given as 25, 30, 32, 30, 42, 45, 48, 50, 52, 51, 42, 38, 40, and 42. What is the mode of the given data?
