Vector Space- Subspace

This picture shows a set of points in the plane  $\mathbb{R}^2$  . Which of the following axioms of a vector space is NOT satised for this set?

• Closure under Addition

• Additive Identity.

• Additive Inverses.

• None of the above.

The picture shows a set of points in the plane  $\mathbb{R}^2$   .
Which of the following axioms of a vector space is
NOT satised for this set?

• Closure under Addition.

• Additive Identity.

• Additive Inverses.

• None of the above.

Which of the following axioms of a vector space is NOT satised for this set of 2  1 matrices with the operations of matrix addition and scalar multiplication?

• Closure under scalar multiplication.

• Additive Identity.

• Additive Inverses.

• None of the above.

The set of all 2x2 matrices with determinant equal to zero under the operations of matrix addition and scalar multiplication is not a vector space. Why?

• 2x2 matrices are not vectors.

• With matrices, AB need not equal BA.

• 
• 
• None of the above.

 $\mathbb{R}^2$  Which of the three sets in the plane is a subspace of
the vector space

• The blue line only.

• The red line only

• The green line only.

• More than one.

• None of them.