please give a brief explanation to why you chose the answers age Linear Algebra

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please give a brief explanation to why you chose the answers

age Linear Algebra Hw1 Spring20... 274 5. If one multiplies a row vector by a column vector, one gets O A. A number. O B. A column vector. ° C. A number, if the two vectors have the same length, and nothing undefined) otherwise. 0 D. An L-shaped vector. 0 E. Nothing; this operation cannot be defined in general. ° F. A matrix. O G. A row vector. 6. If one adds a row vector to a column vector, one gets 0 A. A matrix. O B. Nothing; this operation cannot be defined in general. ° C. A row vector. 0 D. An L-shaped vector. E.A number. F. A column vector.

Explanation / Answer

5) Let the order of row vector be 1xn and the order of column vector be mx1;
Now these 2 matrices can be multiplied if n=m i.e. they have the same length; In this case it will result in a matrix of order 1x1 else if m is not equal to n then it cannot be multiplied;  
Hence, answer is option (c)

6) Two matrices can be added if they have the same order;
Since a column vector and row vector do not have the same order, this operation cannot be defined in general (unless it's a 1x1 order in which case it will be a number);
Hence, answer is option (b)

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