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Exercise 1.2.22

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$v_{1}^{2} w_{1}^{2} + 2 v_{1} w_{1} v_{2} w_{2} + v_{2}^{2} w_{2}^{2} \leq v_{1}^{2} w_{1}^{2} + v_{1}^{2} w_{2}^{2} + v_{2}^{2} w_{1}^{2} + v_{2}^{2} w_{2}^{2}$ is true (cancel 4 terms) because the difference is $v_{1}^{2} w_{2}^{2} + v_{2}^{2} w_{1}^{2} - 2 v_{1} w_{1} v_{2} w_{2}$ which is ${(v_{1} w_{2} - v_{2} w_{1})}^{2} \geq 0$

mathchakra

2021-11-20 14:08

Exercise 1.2.22

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