Let T: set of real numbers R Superscript nℝnright arrow→set of real numbers R Superscript mℝm be a linear transformation, and let {v1, v2, v3} be a linearly dependent set in set of real numbers R Superscript nℝn. Explain why the set {T(v1), T(v2), T(v3)} is linearly dependent.

is linearly dependent set.

Step-by-step explanation:

Given:   is a linearly dependent set in set of real numbers R

To show: the set is linearly dependent.

Solution:

If is a set of linearly dependent vectors then there exists atleast one such that

Consider

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

1.

2.

Here, ∈ U

As T is a linear transformation,

As is a linearly dependent set,

for some

So, for some

Therefore, set is linearly dependent.

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: )

step-by-step explanation:

a

step-by-step explanation:

the answer is a