AMTH FINAL

Let “W” be a set of vectors in R^N. According to the definition, which one of the following is NOT a property of “W” being a subspace?

The zero vector R^N of is not contained in W.

If ( v1, v2, v3 .. ) are vectors in R^N, then Span ( v1, v2, v3 .. ) is a subspace of R^N.

True

For each subset of the xy-plane, decide if it is a subspace of R²

The set of points where y = 0

Subspace of R²

For each subset of the xy-plane, decide if it is a subspace of R²

The set of points where x = 0

Subspace of R²

For each subset of the xy-plane, decide if it is a subspace of R²

The set of points where x >= 0

NOT Subspace of R²

For each subset of the xy-plane, decide if it is a subspace of R²

The set of points where x = 0 and y = 0

Subspace of R²

For each subset of the xy-plane, decide if it is a subspace of R²

The set of points where x = 4

NOT Subspace of R²

Let S be the set of vectors in R³ whose first component is 1. Select all of the following that are true

• S is closed under vector addition

• S is closed under scalar multiplication

  • S is a subspace of R³
    
    NONE OF THE ABOVE

Let S be the set of vectors in whose first component is zero. Select all of the following that are true:

• S is closed under vector addition

• S is closed under scalar multiplication

• S is a subspace of R³

Select the subset(s) of some vector spaces that are subspaces.

All polynomials of degree three or less that have no t² term.

The set of all vectors in R² of the form x (1,5) + x² (5,1) where x1, x2 are real numbers

Which of the following is not a subspace of R²?

The set (2,-3).

The set containing the points on the graph of the line y = 2X -3.

A matrix 10 × 8 has 6 pivot positions. What can you say about the linear independence of its columns?

They are linearly dependent

A 5 × 9 matrix has 4 pivot positions. What can be said about the linear independence of its rows?

They are linearly dependent