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Coursera: Machine Learning (Week 1) Quiz - Linear Algebra | Andrew NG

▸ Linear Algebra :

  1. Let two matrices be
    ,
    What is A - B ?






  1. Let two matrices be
    ,
    What is A + B ?

  1. Let

    What is 2∗x ?


    • Correct
      To multiply the vector x by 2, take each element of x and multiply that element by 2.









  1. Let

    What is 2∗x ?



    • Correct
      To multiply the vector x by 2, take each element of x and multiply that element by 2.



  1. Let u be a 3-dimensional vector, where specifically

    What is ?







  1. Let u and v be 3-dimensional vectors, where specifically

    and

    what is ?
    (Hint: is a 1x3 dimensional matrix, and v can also be seen as a 3x1 matrix. The answer you want can be obtained by taking the matrix product of and .) Do not add brackets to your answer.
    -4
    


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  1. Let A and B be 3x3 (square) matrices. Which of the following must necessarily hold true? Check all that apply.

    • If A is the 3x3 identity matrix, then
      Correct
      Even though matrix multiplication is not commutative in general ( for general matrices A,B), for the special case where , we have , and also . So, .


    • Correct
      We add matrices element-wise. So, this must be true.

  1. Let A and B be 3x3 (square) matrices. Which of the following must necessarily hold true? Check all that apply.
    • If , then C is a 3x3 matrix.
      Correct
    • If A is the 3x3 identity matrix, then
      Correct
      Even though matrix multiplication is not commutative in general ( for general matrices A,B), for the special case where , we have , and also . So, .



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