question about vector multiplication

The Matlab vector v1 has a dimension of n-by-1 and the vector v2 has a dimension of 1-by-n, which of the following is true?

A) The+operation v1*v2 does+not+return+an+error

B) The+operation v2*v1 does+not+return+an+error

C) The+operation v1.*v2 does+not+return+an+error

D) None+of+the+above

[Steven Lord]

Since this sounds like a homework (or maybe an exam) question, what do you think the answer is and why do you think that's the answer?

[Judy Zhuo]

the answer is A but idk why I tried with matlab and all three work

[David Goodmanson]

Hello JZ,

If anyone is saying that A is correct but B is not, they are mistaken. Both A and B are true, with A returning an NxN matrix and B returning a scalar. That's standard matrix algebra.

I am a bit surprised that C, element-by-element multiplication, returns an answer. I thought that it would error out. For the product of an NxM matrix and an MxN matrix it does error out for N~=M, N >1, M >1, i.e. v1 and v2 are matrices rather than simple vectors.

[Judy Zhuo]

The question said A and B are vectors

[Walter Roberson]

v1.*v2 is an example of implicit expansion as of R2016b.

The question said A and B are vectors

Yes, but the question talks about returning an error, not about whether the result is an array, a vector, or a scalar.

>> v1 = rand(5,1); v2 = rand(1,5);
>> v1*v2

ans =

         0.772181449374705         0.136904501442802         0.406952626197035         0.883582709529619         0.764391769792849
         0.126134670907917        0.0223631430789796        0.0664750954870026         0.144331898126657         0.124862238539422
          0.77674644648747         0.137713856102018         0.409358456543161         0.888806290750275         0.768910715728357
         0.766002014144726         0.135808913741177         0.403695959778422          0.87651177804287         0.758274672010212
         0.388436651747121        0.0688681736560934         0.204712656160906         0.444475724597195         0.384518146507958

>> v2*v1

ans =

          2.46493297354767

>> v1.*v2

ans =

         0.772181449374705         0.136904501442802         0.406952626197035         0.883582709529619         0.764391769792849
         0.126134670907917        0.0223631430789796        0.0664750954870026         0.144331898126657         0.124862238539422
          0.77674644648747         0.137713856102018         0.409358456543161         0.888806290750275         0.768910715728357
         0.766002014144726         0.135808913741177         0.403695959778422          0.87651177804287         0.758274672010212
         0.388436651747121        0.0688681736560934         0.204712656160906         0.444475724597195         0.384518146507958

No errors.

[Judy Zhuo]

Thanks

Answer 1

[Sourav Bairagya]

The first two options of your question are performing matrix multiplication of the vectors A and B by considering them nX1 and 1Xn matrices respectively. In first case it will produce a nXn matrix and in 2nd case it will give 1X1 matrix i.e. a scalar.

In 3rd option, it is the case of element-wise multiplication.

C = A.*B performs the element-wise multiplication of vectors A and B, where either A and B are of same size or having compatible sizes. If A and B have compatible sizes, then the two vector implicitly expand to match each other.

Like, if one of them is a scalar, then the scalar is combined with each element of the other vector. Also, vectors with different orientations (one row vector and one column vector) implicitly expand to form a matrix. Hence, in these cases, this elememt-wise multiplications will sucessfully performed without throwing any error.

To know more about the compatible sizes of two vectors, you can leverage the following link:

https://www.mathworks.com/help/matlab/matlab_prog/compatible-array-sizes-for-basic-operations.html