Question

What does Cauchy-Schwarz inequality tell us?

• A. $\left({\sum }_i\right(a_i{)}^2)+({\sum }_i\left(b_i{)}^2\right)\ge ({\sum }_i{a}_i{b}_i{)}^2$
• B. $\left({\sum }_i\right(a_i{)}^2)-({\sum }_i\left(b_i{)}^2\right)\ge ({\sum }_i{a}_i{b}_i{)}^2$
• C. $\left({\sum }_i\right(a_i{)}^2)\times ({\sum }_i\left(b_i{)}^2\right)\ge ({\sum }_i{a}_i{b}_i{)}^2$
• D. None of the above

Answer 1

Answer: (C)

$\left({\sum }_i\right(a_i{)}^2)\times ({\sum }_i\left(b_i{)}^2\right)\ge ({\sum }_i{a}_i{b}_i{)}^2$

Cauchy-Schwarz inequality states that

${\sum }_i{a}_i^2\times {\sum }_i{b}_i^2\ge ({\sum }_i{a}_i{b}_i{)}^2$