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Marianna [84]
3 years ago
6

wilhelmina has 8.3 ounces of peanut butter.if she makes 5 sandwijes with an equal amount ofbpeanut butter on each,how much peanu

t butter does she put on each one?
Mathematics
1 answer:
kotykmax [81]3 years ago
3 0

Peanut butter: 8.3 ounces

Sandwich: 5

Divide 8.3 by 5, for equal amount of peanut butter on each sandwich.

8.3/5 = 1.66

She puts 1.66 ounces of peanut butter on each sandwich.

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Answer:

\{T(v_1), T(v_2), T(v_3)\} is linearly dependent set.

Step-by-step explanation:

Given:  \{v_1,v_2,v_3\} is a linearly dependent set in set of real numbers R

To show: the set \{T(v_1), T(v_2), T(v_3)\} is linearly dependent.

Solution:

If \{v_1,v_2,v_3,...,v_n\} is a set of linearly dependent vectors then there exists atleast one k_i:i=1,2,3,...,n such that k_1v_1+k_2v_2+k_3v_3+...+k_nv_n=0

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A linear transformation T: U→V satisfies the following properties:

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As T is a linear transformation,

k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0\\T(k_1v_1)+T(k_2v_2)+T(k_3v_3)=0\\T(k_1v_1+k_2v_2+k_3v_3)=0\\

As \{v_1,v_2,v_3\} is a linearly dependent set,

k_1v_1+k_2v_2+k_3v_3=0 for some k_i\neq 0:i=1,2,3

So, for some k_i\neq 0:i=1,2,3

k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0

Therefore, set \{T(v_1), T(v_2), T(v_3)\} is linearly dependent.

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