Linear Algebra

38 Questions | Attempts: 230
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  • 1/38 Questions

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

    • True
    • False
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Linear Algebra - Quiz

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  • 2. 

    A null space is a vector space.

    • True

    • False

    Correct Answer
    A. True
  • 3. 

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

    • True

    • False

    Correct Answer
    A. True
  • 4. 

    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.

    • True

    • False

    Correct Answer
    A. True
  • 5. 

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

    • True

    • False

    Correct Answer
    A. True
  • 6. 

    If A or B is singular then AB is singular as well. (Use properties of the determinant to decide)

    • True

    • False

    Correct Answer
    A. True
  • 7. 

    The dimension of the column space of A is the number of columns in RREF(A) that contain leading ones.

    • True

    • False

    Correct Answer
    A. True
  • 8. 
    For a nonzero scalar , the vector is times a s long as and has the same direction as - ProProfs

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

    • True

    • False

    Correct Answer
    A. True
  • 9. 

    If one row of a square matrix is a multiple of another row, then the determinant of that square matrix is zero.

    • True

    • False

    Correct Answer
    A. True
  • 10. 
    If 0 is an eigenvalue of a matrix then is singular. - ProProfs

    If 0 is an eigenvalue of a matrix then is singular.

    • True

    • False

    Correct Answer
    A. True
  • 11. 

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

    • True

    • False

    Correct Answer
    A. True
  • 12. 
    If is an eigenvector of with eigenvalue then any multiple of is also an eigenvector of with eigenvalue . - ProProfs

    If is an eigenvector of with eigenvalue then any multiple of is also an eigenvector of with eigenvalue .

    • True

    • False

    Correct Answer
    A. True
  • 13. 

    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.

    • True

    • False

    Correct Answer
    A. True
  • 14. 
    The matrix    is non-singular. - ProProfs

    The matrix    is non-singular.

    • True

    • False

    Correct Answer
    A. True
  • 15. 

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

    • True

    • False

    Correct Answer
    A. True
  • 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).

    • True

    • False

    Correct Answer
    A. True
  • 17. 
    If is a square matrix and for some nonzero vector then is an eigenvector of . - ProProfs

    If is a square matrix and for some nonzero vector then is an eigenvector of .

    • True

    • False

    Correct Answer
    A. True
  • 18. 
    If the characteristic polynomial of a matrix is then is invertible. - ProProfs

    If the characteristic polynomial of a matrix is then is invertible.

    • True

    • False

    Correct Answer
    A. True
  • 19. 

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

    • True

    • False

    Correct Answer
    A. True
  • 20. 

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

    • True

    • False

    Correct Answer
    A. True
  • 21. 
    The column space of an matrix is in Rm. - ProProfs

    The column space of an matrix is in Rm.

    • True

    • False

    Correct Answer
    A. True
  • 22. 
    If the determinant of the matrix A is 6 then the homogeneous linear system with A as its coefficient matrix has only the trivial (all zeros) solution. - ProProfs

    If the determinant of the matrix A is 6 then the homogeneous linear system with A as its coefficient matrix has only the trivial (all zeros) solution.

    • True

    • False

    Correct Answer
    A. True
  • 23. 

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

    • True

    • False

    Correct Answer
    A. False
  • 24. 

    Subspace? {(u1, u2, u3, u4) in R4 such that 3u1+2u2=0}

    • True

    • False

    Correct Answer
    A. True
  • 25. 

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

    • True

    • False

    Correct Answer
    A. True
  • 26. 

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

    • True

    • False

    Correct Answer
    A. False
  • 27. 

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

    • True

    • False

    Correct Answer
    A. True
  • 28. 

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

    • True

    • False

    Correct Answer
    A. False
  • 29. 

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

    • True

    • False

    Correct Answer
    A. False
  • 30. 

    Subspace? {(u1, u2, u3) in R3 such that u1 is greater than u2}

    • True

    • False

    Correct Answer
    A. False
  • 31. 
    Subspace? {(u1,u2) in R2 such that u12+u22 is less than or equal to 1} - ProProfs

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

    • True

    • False

    Correct Answer
    A. False
  • 32. 

    In general the determinant of the sum of two matrices equals the sum of the determinants of the matrix.

    • True

    • False

    Correct Answer
    A. False
  • 33. 

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

    • True

    • False

    Correct Answer
    A. False
  • 34. 

    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.

    • True

    • False

    Correct Answer
    A. False
  • 35. 
    If is an eigenvalue of a matrix , then the linear system has only the trivial solution. - ProProfs

    If is an eigenvalue of a matrix , then the linear system has only the trivial solution.

    • True

    • False

    Correct Answer
    A. False
  • 36. 
    The following linear system has a unique solution. - ProProfs

    The following linear system has a unique solution.

    • True

    • False

    Correct Answer
    A. False
  • 37. 

    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.

    • True

    • False

    Correct Answer
    A. False
  • 38. 

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

    • True

    • False

    Correct Answer
    A. False

Quiz Review Timeline (Updated): Oct 23, 2012 +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

  • Current Version
  • Oct 23, 2012
    Quiz Edited by
    ProProfs Editorial Team
  • Oct 22, 2012
    Quiz Created by
    MarkusRibasTest
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