Using a specific example, prove the vector property: For vectors u⃗ and v⃗ and scalar p > 1, show p(u⃗ +v⃗ )=pu⃗ +pv⃗ . It works for all p-values, but I am asking you to narrow your examples to a semi-specific example.

Question

Using a specific example, prove the vector property: For vectors u⃗ and v⃗ and scalar p > 1, show p(u⃗ +v⃗ )=pu⃗ +pv⃗ . It works for all p-values, but I am asking you to narrow your examples to a semi-specific example.

(the box next to the letter means its a vector)

Answer 1

let u=i + 3j

v= 4i + j
let p=10

p((u⃗ +v⃗ ) =?= pu⃗ +pv⃗
10(i+3j+4i+j)=?=10i+30j+40i+10j
10(5i+4j)=?=50i+40j
50i+40j does = 50i+40j

Answer 2

To prove the vector property p(u⃗ + v⃗) = pu⃗ + pv⃗, we need to demonstrate this property using a semi-specific example. Let's consider the vectors u⃗ = [1, 2] and v⃗ = [3, 4], and let p = 2.

Using these values, we can calculate both sides of the equation and see if they are equal.

Left side of the equation: p(u⃗ + v⃗)
Substituting the values: 2([1, 2] + [3, 4])
Adding the vectors: 2([1+3, 2+4])
Calculating: 2([4, 6])
Result: [8, 12]

Right side of the equation: pu⃗ + pv⃗
Substituting the values: 2[1, 2] + 2[3, 4]
Calculating: [2, 4] + [6, 8]
Adding the vectors: [2+6, 4+8]
Result: [8, 12]

By comparing the results, we can see that the left side of the equation (p(u⃗ + v⃗)) is equal to the right side (pu⃗ + pv⃗). Therefore, we have successfully proven the vector property for this semi-specific example.

Using a specific example, prove the vector property: For vectors u⃗ and v⃗ and scalar p > 1, show p(u⃗ +v⃗ )=pu⃗ +pv⃗ . It works for all p-values, but I am asking you to narrow your examples to a semi-specific example.

let u=i + 3j

thanks

To prove the vector property p(u⃗ + v⃗) = pu⃗ + pv⃗, we need to demonstrate this property using a semi-specific example. Let's consider the vectors u⃗ = [1, 2] and v⃗ = [3, 4], and let p = 2.