SB Matching Exercises

Each putative basis is a subset of exactly one of the three subspaces. So for each subspace, two of the three sets can be ruled out by simply testing that the vectors of the basis are members of the subspace, via the membership criteria.

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${⟨ x, y, z ⟩ ∣ - y + z = 0}$
${⟨ - 4, 3, 3 ⟩, ⟨ 3, - 2, - 2 ⟩}$
${⟨ x, y, z ⟩ ∣ - 3 x - 5 y + z = 0}$
${⟨ - 4, 3, 3 ⟩, ⟨ 5, - 4, - 5 ⟩}$
${⟨ x, y, z ⟩ ∣ - 2 x - 5 y + 2 z = 0}$
${⟨ 3, - 2, - 2 ⟩, ⟨ 5, - 4, - 5 ⟩}$

Hint.

For openers, a basis for a subspace must be a subset of the subspace.

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4. Matching Problem, Function Types.

Sort the following functions into their correct categories.

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Review Active Prelude to Calculus

A precalculus textbook that could help

url.

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$y = 5 x + 3$
$π x - 6 y = \sqrt{2}$
$y = \frac{- 1}{2} x + e$
Linear
Quadratic
$y = x^{3} - x$
$y = 2^{x}$
Exponential
$y = x^{3}$
$y = \sqrt{x}$
Power

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