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Contact [7]
2 years ago
7

Suppose that L1 : V → W and L2 : W → Z arelinear transformations and E, F, and G are orderedbases for V, W, and Z, respectively.

Show that, if Arepresents L1 relative to E and F and B representsL2 relative to F and G, then the matrix C = BA representsL2 ◦ L1: V → Z relative to E and G. Hint:Show that BA[v]E = [(L2 ◦ L1)(v)]G for all v ∈ V.

Mathematics
1 answer:
daser333 [38]2 years ago
3 0

Answer:

a) v ∈ ker(<em>L</em>) if only if [V]_{E} ∈ <em>N</em>(<em>A</em>)

b) w ∈ <em>L</em>(<em>v</em>) if and only if [W]_{F} is in the column space of <em>A</em>

<em />

<em>See attached</em>

Step-by-step explanation:

See attached the proof Considering the vector spaces <em>V</em> and <em>W</em> with other bases <em>E</em> and <em>F</em> respectively.

Let <em>L</em> be the Linear transformation form <em>V</em> and <em>W</em> and A is the matrix representing <em>L</em> relative to<em> E</em> and <em>F</em>

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