Short Answer TypeIf A is a 3 × 3 invertible matrix, then what will be the value of k if det(A–1) = (det A)k.
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of the z-axis.
The volume of a sphere is increasing at the rate of 3 cubic centimetres per second. Find the rate of increase of its surface area, when the radius is 2 cm.
Show that the function f(x) = 4x3 – 18x2 + 27x – 7 is always increasing on R.
The given function is f(x) =4x3 – 18x2 + 27x – 7
On differentiating both sides with respect to x, we get
f'(x) = 12x2-36x +27
⇒ f'(x) = 3(4x2-12x+9)
⇒ f'(x) = 3(2x-3)2
Which is always positive for all x ε R.
Since, f'(x) ≥ 0 ∀ x ε R,
Therefore, f(x) is always increasing on R.
is continuous at x = 0.
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find a matrix D such that CD – AB = O.
