Practice for Linear Algebra's Final Exam

If is a square matrix, then the statement that MAY be True is...

• all answers may be True

If A is of size n x n and rank(A) = n, then the column vectors of A are linearly independent.

• True

• False

If D is a diagonal matrix in the size of n x n and Rank(D) = n-1, then there is a 0 in the main diagonal

• True

• False

If Ax = 0 is an underdetermined homogenous SLE, then nullity(A) must be positive

• True

• False

If the size of matrix A is 4 x 7, then the statement that is always true is ...

• Nullity(A) = 6

• Nullity(A) >= 3

• Nullity(A) < 3

• Nullity(A) = 4

If A is a square matrix and SLE Ax=b has exactly one solution, then Row(A) = Coll(A)

• True

• False

Given the following matrix, the correct statement is ...

• Rank(A) = 2 and Nullity(A) = 2

• Rank(A) = 1 and Nullity(A) = 3

• Rank(A) = 0 and Nullity(A) = 3

• Rank(A) = 3 and Nullity(A) = 1

Given vector space R^3 and any vector a = (a1, a2, a3) and b = (b1, b2, b3), the function that is an inner product in R^3 is ...

• b₁ + a₂b₂ +3a₃b₃

• 2a₁b₁ +a₂b₂

• 4a₁b₁ + a₂b₂ - a₃b₃

• a₁b₁ + 2a₂b₂ + a₃b₃

Property of vector length in Euclidean space is ....

Unit vector that is orthogonal to (-1, 1) is ...