A set in R2 is displayed to the right. Assume the set includes the bounding lines. Give a specific reason why the set H is not a subspace of R. (For instance, find two vectors in H whose sum is not in H, or find a vector in H with a scalar multiple that is not in H. Draw a picture.) Let u and v be vectors and let k be a scalar. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. В. D. The set is not a subspace because it is closed under sums, but not under The set is not a subspace because it is not closed under either scalar The set is not a subspace because it does not include the zero vector. The set is not a subspace because it is closed under scalar multiplication, but not under sums. For example, the sum of (3,1) and (1,3) is not in the set. multiplication or sums. For example, scalar multiplication. For example, multiplied by (1,1) is not in the set. multiplied by (1,3) is not in the set, and the sum of (3,1) and (1,3) is not in the set. ku u+v u+v/ ku
A set in R2 is displayed to the right. Assume the set includes the bounding lines. Give a specific reason why the set H is not a subspace of R. (For instance, find two vectors in H whose sum is not in H, or find a vector in H with a scalar multiple that is not in H. Draw a picture.) Let u and v be vectors and let k be a scalar. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. В. D. The set is not a subspace because it is closed under sums, but not under The set is not a subspace because it is not closed under either scalar The set is not a subspace because it does not include the zero vector. The set is not a subspace because it is closed under scalar multiplication, but not under sums. For example, the sum of (3,1) and (1,3) is not in the set. multiplication or sums. For example, scalar multiplication. For example, multiplied by (1,1) is not in the set. multiplied by (1,3) is not in the set, and the sum of (3,1) and (1,3) is not in the set. ku u+v u+v/ ku
A set in R2 is displayed to the right. Assume the set includes the bounding lines. Give a specific reason why the set H is not a subspace of R. (For instance, find two vectors in H whose sum is not in H, or find a vector in H with a scalar multiple that is not in H. Draw a picture.) Let u and v be vectors and let k be a scalar. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. В. D. The set is not a subspace because it is closed under sums, but not under The set is not a subspace because it is not closed under either scalar The set is not a subspace because it does not include the zero vector. The set is not a subspace because it is closed under scalar multiplication, but not under sums. For example, the sum of (3,1) and (1,3) is not in the set. multiplication or sums. For example, scalar multiplication. For example, multiplied by (1,1) is not in the set. multiplied by (1,3) is not in the set, and the sum of (3,1) and (1,3) is not in the set. ku u+v u+v/ ku
Transcribed Image Text:A set in R< is displayed to the right. Assume the set includes the bounding lines. Give a specific reason why the set H is not a subspace of R.
(For instance, find two vectors in H whose sum is not in H, or find a vector in H with a scalar multiple that is not in H. Draw a picture.)
Let u and v be vectors and let k be a scalar. Select the correct choice below and, if necessary, fill in the answer box within your choice.
A.
В.
С.
D.
The set is not a subspace because it is
closed under sums, but not under
The set is not a subspace because it is
The set is not a subspace because it
does not include the zero vector.
The set is not a subspace because it is
closed under scalar multiplication, but
not under sums. For example, the sum
of (3,1) and (1,3) is not in the set.
not closed under either scalar
scalar multiplication. For example,
multiplication or sums. For example,
multiplied by (1,1) is not in the set.
multiplied by (1,3) is not in the set,
and the sum of (3,1) and (1,3) is not in
the set.
ku
u+v
u+y
ku
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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