Let $S$ be a subset in $M_{2x2}$; $a - 3d = 0$ and $b + c = 0$ with the standard operations in $M_{2x2}$. Which of the following is true? $S$ is not a subspace of $M_{2x2}$ since $z \notin S$. The above is true. The above is true. $S$ is a subspace of $M_{2x2}$. None of these. The above is true.
Added by Kent B.
Close
Step 1
A subset $S$ of a vector space $V$ is called a subspace if it satisfies three conditions: Show more…
Show all steps
Your feedback will help us improve your experience
Maria Dearborn and 63 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Let W1 and W2 be subspaces of a vector space V for which W1 ⊂ W2. Let W = W1 ∪ W2. Then, which of the following is always true? a) W ⊃ V b) V is a subspace of W c) W is a subspace of V d) W = ∅
Adi S.
Which of the following subsets of R^2 are subspaces of R^2? Justify each answer briefly - if the set is a subspace, show how you know; and if the set is not a subspace, give an example of a 'subspace condition' that the set fails to satisfy:
Shaiju T.
Determine whether the set $W$ is a subspace of $R^{3}$ with the standard operations. Justify your answer. $W=\{(a, a-3 b, b): a \text { and } b \text { are real numbers }\}$
Vector Spaces
Subspaces of Vector Spaces
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Watch the video solution with this free unlock.
EMAIL
PASSWORD