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lana [24]
2 years ago
11

Let T : V → W be a linear transformation from vector space V into vector space W.

Mathematics
1 answer:
wel2 years ago
7 0

Explanation:

Since {v1,...,vp} is linearly dependent, there exist scalars a1,...,ap, with not all of them being 0 such that a1v1+a2v2+...+apvp = 0. Using the linearity of T we have that

a1*T(v1)+a2*T(v1) + ... + ap*T(vp) = T(a1v19+T(a2v2)+...+T(avp) = T(a1v1+a2v2+...+apvp) = T(0) = 0.

Since at least one ai is different from 0, we obtain a non trivial linear combination that eliminates T(v1) , ..., T(vp). That proves that {T(v1) , ..., T(vp)} is a linearly dependent set of W.

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3 0
3 years ago
Tammy baked a batch of 20 cupcakes. Daniella baked
ElenaW [278]

Multiplication is the process of multiplying. The total number of cupcakes that are produced by the 3 girls is 44.

<h3>What is multiplication?</h3>

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given that Tammy baked a batch of 20 cupcakes and Daniella baked 4/5 as many cupcakes as Tammy. Therefore, the number of cupcakes made by Daniella is,

Number of cupcakes made by Daniella

= (4/5)×(Number of cupcakes made by Tammy)

= (4/5) × 20

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Now, if Miko baked 1/2 as many cupcakes as Daniella. Therefore, the number of cupcakes made by Miko is,

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= (1/2) × (Number of cupcakes made by Daniella)

= (1/2) × 16

= 8

Further, the total number of cupcakes that are produced are,

Number of cupcakes = 20 + 16 + 8 = 44

Hence, the total number of cupcakes that are produced by the 3 girls is 44.

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