# Linear Algebra

38 Questions | Total Attempts: 121  Settings  Related Topics
• 1.
The dimension of the column space of A is the number of columns in RREF(A) that contain leading ones.
• A.

True

• B.

False

• 2.
The dimension of the column space of A and the null space of A add up to the number of rows in A.
• A.

True

• B.

False

• 3.
If a set of p vectors spans a p-dimensional subspace H of Rn, then these vectors forma basis for H.
• A.

True

• B.

False

• 4.
The dimension of the null space of A is the number of variables (xi) in the equation Ax=0.
• A.

True

• B.

False

• 5.
The dimension of the column space of A is the rank of A.
• A.

True

• B.

False

• 6.
If H is a p-dimensional subspace of Rn, then a linearly independent set of p vectors in H must form a basis for H.
• A.

True

• B.

False

• 7.
A null space is a vector space.
• A.

True

• B.

False

• 8.
The column space of an matrix is in Rm.
• A.

True

• B.

False

• 9.
If u and v are linearly independent, and if w is in Span{u,v} then {u,v,w} is linearly dependent.
• A.

True

• B.

False

• 10.
If three vectors in R3 lie in the same plane in R3, then they are linearly dependent.
• A.

True

• B.

False

• 11.
If a set of vectors from Rn contains fewer than n vectors, then the set is linearly independent.
• A.

True

• B.

False

• 12.
If v1 and v2 are vectors in R4 and v2 is not a scalar multiple of v1 then {v1,v2} is linearly independent.
• A.

True

• B.

False

• 13.
If v1, v2, v3 are in R3 and v3 is not a linear combination of v1, v2, then {v1,v2,v3} is linearly independent.
• A.

True

• B.

False

• 14.
If {v1,..., v4} is a linearly independent set of vectors in R4 then {v1,v2,v3} is also linearly independent.
• A.

True

• B.

False

• 15.
For a nonzero scalar , the vector is times a s long as and has the same direction as
• A.

True

• B.

False

• 16.
The vector (10, 30, -13, 14, -7, 27) can be written as a linear combination of the vectors (1,2,-3,4,-1,2), (1,-2,1,-1,2,1), (0, 2, -1, 2, -1, -1), (1,0,3,-4,1,2), and (1, -2, 1, -1, 2, -3).
• A.

True

• B.

False

• 17.
You can show that a subset of Rn is a subspace of Rn by giving specific numeric examples for which the vectors sum to a vector in the space and for which the negative of the vector is in the space.
• A.

True

• B.

False

• 18.
You can show that a subset of Rn is not a subspace of Rn by giving specific numeric examples for which the vectors do not sum to a vector in the space or for which the negative of the vector is not in the space.
• A.

True

• B.

False

• 19.
If W is a subspace of R2 then W must contain the vector (0,0).
• A.

True

• B.

False

• 20.
If W and U are subspaces of R2 then the union (collection of all vectors in either W or U or both) is also a subspace of R2.
• A.

True

• B.

False

• 21.
Subspace? {(u1,u2) in R2 such that u1u2=0}
• A.

True

• B.

False

• 22.
Subspace? {(u1,u2) in R2 such that u12+u22 is less than or equal to 1}
• A.

True

• B.

False

• 23.
Subspace? {(2s-2, 2s+4t, -t) in R3 such that s and t are real numbers}
• A.

True

• B.

False

• 24.
Subspace? {(2s, 2s+4t, -t) in R3 such that s and t are real numbers}
• A.

True

• B.

False

• 25.
Subspace? {(u1, u2, u3) in R3 such that u1 is equal to u2}
• A.

True

• B.

False