Question

State whether the following statement are TRUE or FALSE. Give reason in support of your answer.
a) Derivative of 1/x with respect to x is 1. 
b) If A is a matrix of order 2 by 3 and B is a matrix of order 3 by 2, then order of the matrix A + B is 2 by 3.
c) If overrightarrow{a} = 3hat{i} - 5hat{j} + 4hat{k} and overrightarrow{b} = 4hat{i} + 4hat{j} + 2hat{k} they are perpendicular to each other.
d) If probability of an event E is 1/2 and probability of the event E cap B is 1/6, then probability of the event F is 1/3, where events E and F are independent.
e) If the first term of an AP is 5 and 101 term of the AP is 1005 then common difference of the AP will be 105

13 Jul 2024
Answer :
Word Count : 455
Let's analyze each statement one by one: ### a) Derivative of 1/x with respect to x is 1. **FALSE**. The derivative of \( \frac{1}{x} \) with respect to \( x \) is not 1. We can find the derivative using basic differentiation rules: \[ \frac{d}{dx}\left(\frac{1}{x}\right) = \frac{d}{dx}\left(x^{-1}\right) = -x^{-2} = -\frac{1}{x^2} \] ### b) If A is a matrix of order 2 by 3 and B is a matrix of order 3 by 2, then ________ _______ _________ ____ __________ ____.
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