3 years ago

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Mathematics

1 answer:

mash [69]3 years ago

5 0

Answer:a is 14, b is 70%, c is 250

Step-by-step explanation:

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Use mathematical induction to prove that if L is a linear transformation from V to W, then L (α1v1 + α2v2 +· · ·+αnvn)= α1L (v1)

e-lub [12.9K]

Answer:

The proof is shown in the explanation below.

Step-by-step explanation:

Analysis:

The proof by induction focuses on n. In this case, let n = 1, and $L^{1}$ will be a linear operator since $L^{1} = L$

The exercise will show that $L^{n}$ is a linear operator on V and that $L^{n+1}$ is also a linear operator on V. This, follows that:

$L^{n+1} (av) = L(L^{m}(v_{1}+v_{2})\\ = L(L^{m} (v_{1} + L^{m}v_{2})\\ = L(L^{m}v_{1} + L(L^{m}v_{2})\\ = L^{m+1}(v_{1}) + L^{m+1}(v_{2})$

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3 years ago

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Which of the following descriptions represents the transformation shown in the image

Viktor [21]

Answer: A. 270° rotation, 3 units left, and 2 units up

<u>Step-by-step explanation:</u>

C = (1, 1) D = (3, 3) E = (2, -2)

270° rotation counterclockwise means (x, y) = (y, -x)

new C = (1, -1) new D = (3, -3) new E = (-2, -2)

3 units left means subtract 3 from the x-coordinate

newer C =( -2, -1) newer D = (0, -3) newer E = (-5, -2)

2 units up means add 2 to the y-coordinate

C' = (-2, 1) D' = (0, -1) E' = (-5, 0)

Since the first option worked, there is no need to check the other options.

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3 years ago

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