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lutik1710 [3]
3 years ago
15

Find u, v , u , v , and d(u, v) for the given inner product defined on Rn. u = (0, −4), v = (5, 3), u, v = 3u1v1 + u2v2

Mathematics
1 answer:
tigry1 [53]3 years ago
7 0

Answer:

=-12

d(u,v)=2\sqrt{31}

Step-by-step explanation:

We are given that inner product defined on R_n

=3u_1v_1+u_2v_2

u=(0,-4),v=(5,3)

We have to find the value of <u,v> and d(u,v)

We have u_1=0,u_2=-4,v_1=5,v_2=3

Substitute the value then we get

=3(0\cdot5)+(-4)(3)=-12

Now, d(u,v)=\left \|v-u\right \|

Using this formula we get

d(u,v)=\left \| (5,7) \right \|=\sqrt{3(5)^2+(7)^2}=\sqrt{75+49}=\sqrt{124}

d(u,v)=2\sqrt{31}

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