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Determine which of the following vectors are equal:𝑢1=1,2,3,𝑢2=2,3,1, 𝑢3=1,3,2, 𝑢4=2,3,1

Question

Determine which of the following vectors are equal:

  • u1=(1,2,3) u_1 = (1, 2, 3)
  • u2=(2,3,1) u_2 = (2, 3, 1)
  • u3=(1,3,2) u_3 = (1, 3, 2)
  • u4=(2,3,1) u_4 = (2, 3, 1)
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Solution

To determine if vectors are equal, we need to compare their corresponding components.

Let's compare each vector:

𝑢1 = 1,2,3 𝑢2 = 2,3,1 𝑢3 = 1,3,2 𝑢4 = 2,3,1

Comparing 𝑢1 and 𝑢2, we see that their components are not the same. So, 𝑢1 is not equal to 𝑢2.

Comparing 𝑢1 and 𝑢3, we see that their components are not the same. So, 𝑢1 is not equal to 𝑢3.

Comparing 𝑢1 and 𝑢4, we see that their components are not the same. So, 𝑢1 is not equal to 𝑢4.

Comparing 𝑢2 and 𝑢3, we see that their components are not the same. So, 𝑢2 is not equal to 𝑢3.

Comparing 𝑢2 and 𝑢4, we see that their components are the same. So, 𝑢2 is equal to 𝑢4.

Comparing 𝑢3 and 𝑢4, we see that their components are not the same. So, 𝑢3 is not equal to 𝑢4.

So, the only vectors that are equal are 𝑢2 and 𝑢4.

This problem has been solved

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