Let y : V → W be a linear transformation and let U be a subspace of V. Show that y(U) = {w e W | w = y(u) for some u E U}, the image of U under y, is a subspace of W.

Q: 11. Describe, in words, the transforming effect of the matrix representation of the linear…

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Q: Suppose that F is a linear transformation such that F (1,0,0)= (1,0,1), F (0, 1,0) = (1,-1,3), F…

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Q: Find an orthogonal basis for the subspace Span (1, 1 + x, 1 + x²) ≤ P3. Justify your answer!

A: Using the Gram Schmidt orthogonalisation process:

Q: (d) The set U = [Select] C : a, b, c, d e R, ab = cd is a subspace of R¹.

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Q: What can be said about Nul A if A is a 5×7 ​matrix? Could it be the zero​ subspace? Why or why​ not?

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Q: (a) Prove that the kernel ker(f) of a linear transformation f : V → W is a subspace of V . (b) Prove…

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Q: Discuss what it means to be a subspace and what is required to prove that something is a subspace.…

A: Concept:

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Q: Determine if v is in the subspace of P3 given by span{x + x - 5, x2 + 2x + 1, x-x2 + x}. v = x? + 2x…

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Q: 6) Let T : R" → R™ be a linear transformation. Let X be any subset of the domain. Define T(X) to be…

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Q: Section B: Determine of the following set W is subspace of V=R³: W-{(a, 1, 1): a ER).

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Q: The set of polynomials of degree exactly two is a subspace of P2.

A: False

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Q: TRUE or FALSE: The subset W = {a+bX+cX²: a+b+c= 1} is a subspace of R₂[X]. FALSE TRUE

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Q: Given 7: -9 -10 0 find the closest point to in the subspace W spanned by -5 -6 -4 and 64

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