Question
If A = [1] , then A is:
- Zero matrix
- SIngular matrix
- Non - singular matrix
- Data insufficient
Solution:
$\text{A} = \big[1\big] $ is an identity matrix with order $1\times1.|\text{A}|\neq0$
So A is nonsingular.
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$f(x)=x \cos \frac{1}{x}, \quad x \geq 1,$
$(A)$ for at least one $x$ in the interval $[1, \infty), f(x+2)-f(x)<2$
$(B)$ $\lim _{x \rightarrow \infty} f^{\prime}(x)=1$
$(C)$ for all $x$ in the interval $[1, \infty), f(x+2)-f(x)>2$
$(D)$ $f^{\prime}(x)$ is strictly decreasing in the interval $[1, \infty)$

Statement $II:$ For any $x \in R ,$ ${\sin ^{ - 1}}\,x + {\cos ^{ - 1}}\,x = \frac{\pi }{2}$ and $0 \le {\left( {{{\sin }^{ - 1}}\,x - \frac{\pi }{4}} \right)^2} \le \frac{{9{\pi ^2}}}{{16}}$