The given matrix is
\(u=\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}\)
So 2A = 2\(\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}\)
\(= \begin{bmatrix}2 & 4\\8 & 4\end{bmatrix}\)
so L.H.S. = |2A| \(= \begin{bmatrix}2 & 4\\8 & 4\end{bmatrix}\)
= 2 x 4 - 4 x 8
= 8 - 32
= -24
Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
Determine order and degree(if defined) of differential equation \begin{align} \frac{d^4y}{dx^4}\;+\;\sin(y^m)\;=0\end{align}
Represent graphically a displacement of 40 km, 30° east of north.
If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.
Maximise Z = 3x + 4y
Subject to the constraints:x + y ≤ 4, x ≥ 0, y ≥ 0
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
In Figure, identify the following vectors.
(i) Coinitial (ii) Equal (iii) Collinear but not equal
The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rates of change of (a) the perimeter, and (b) the area of the rectangle.
Show that the function f : R* → R* defined by f(x) = 1/x is one-one and onto,where R* is the set of all non-zero real numbers. Is the result true, if the domain R* is replaced by N with co-domain being same as R* ?
Show that the Signum Function f : R → R, given by
is neither one-one nor onto.
If f(x) = , show that fof(x) = x, for all x ≠ 2/3. What is the inverse of f ?
Let f : R → R be defined as f(x) = 3x. Choose the correct answer.
(A) f is one-one onto
(B) f is many-one onto
(C) f is one-one but not onto
(D) f is neither one-one nor onto.
Plzz give all difficult question.