question about vector multiplication

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Judy Zhuo
Judy Zhuo 2019-12-7
回答： Sourav Bairagya 2019-12-10
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
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Walter Roberson
Walter Roberson 2019-12-7
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.

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回答（1 个）

Sourav Bairagya
Sourav Bairagya 2019-12-10
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

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