Suppose f: A → B, f is one-to-one and onto, and Y c B. Show that the inverse image of Y under f and the image of Y under f1 are equal.

Q: Do question 1 only

A: For any query with the solution, please ask in the comment box.

Q: Find the dim U where -3 4 U = Span 1 -9

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Q: Determine whether the following transformation from R3 to R² is linear.

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Q: Suppose that f : A → B and g : B → C are both injective functions, prove that the function go f : A…

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Q: Let f be the function from {a, b, c, d} to {1, 2, 3, 4} with f(a) = 4, f(b) = 2, f(c) = 1, and f(d)…

A: For bijection, the function needs to be one to one and onto.

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Q: Show that projw is a linear transformation and that (projw)² = projw.

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Q: Let →a=⟨7,−5⟩ and b→=⟨1,3⟩. Compute the dot product. →a X →b=

A: Given a→ = 7,-5 and b→ = 1, 3. We have to compute the dot product a→·b→.

Q: Find the inverse transformation of yi=2x,+x,+x3,y2=x,+x,+2x3,y3=X1-2x3.

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