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Is W a subspace of V? If not, state why. Assume that V has the standard operations. (Select all that apply.) W is the set of all 2 x 2 matrices of the form [88] V = M₂,2 Wis a subspace of V. Ow is not a subspace of V because it is not closed under addition. OW is not a subspace of V because it is not closed under scalar multiplication.

Is W a subspace of V? If not, state why. Assume that V has the standard operations. (Select all that apply.) W is the set of all 2 x 2 matrices of the form [88] V = M₂,2 Wis a subspace of V. Ow is not a subspace of V because it is not closed under addition. OW is not a subspace of V because it is not closed under scalar multiplication.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. 5. Is W a subspace of V? If not, state why. Assume that V has the standard operations. (Select all that apply.) W is the set of all 2 x 2 matrices of the form V = M2,2 O W is a subspace of V. Ow is not a subspace of V because it is not closed under addition. Ow is not a subspace of V because it is not closed under scalar multiplication. The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v3 because 0 = Ov₁ + 0v₂ + 0v3. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of V₁, V₂, and V3. If not possible, enter IMPOSSIBLE.) v₁ = (1, 0, 1), V₂ = (-1, 1, 2), V3 = (0, 7, 2) 0=
Transcribed Image Text:4. 5. Is W a subspace of V? If not, state why. Assume that V has the standard operations. (Select all that apply.) W is the set of all 2 x 2 matrices of the form V = M2,2 O W is a subspace of V. Ow is not a subspace of V because it is not closed under addition. Ow is not a subspace of V because it is not closed under scalar multiplication. The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v3 because 0 = Ov₁ + 0v₂ + 0v3. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of V₁, V₂, and V3. If not possible, enter IMPOSSIBLE.) v₁ = (1, 0, 1), V₂ = (-1, 1, 2), V3 = (0, 7, 2) 0=
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