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kalbaugh
10.02.2021 •
Mathematics
A tree falls down during a thunderstorm and lands on a fence. If the fence is 5 feet tall, and the distance from the base of the fallen tree to the top of the fence (diagonally) is 13 feet, how far away from the fence was the tree before it fell? (Hint: Draw a picture. You are solving for a LEG, not the hypotenuse).
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Ответ:
Let T : V right arrow→ W be a linear transformation from a vector space V into a vector space W. Prove that the range of T is a subspace of W. [Hint: Typical elements of the range have the form T(x) and T(w) for some x and w in V.] What would be the most useful method of proving that the range of T is a subspace of W? A. Show that the three properties that define a subspace are satisfied by the vectors in the range of T. B. Show that there is a set of vectors that span the range of T. C. Show that the range of T must be all of W. D. Find a matrix such that the range of T is the column space of that matrix. E. Find a matrix such that the range of T is the null space of that matrix. F. Show that all ten axioms for a vector space are satisfied by the vectors in the range of T.
Step-by-step explanation: