Please explain why the first one is a scalar and the second one is a vector? thanks !

A special case of matrix multiplication is when A is 1 X n (a row vector) and B is n X 1 (a column vector). For example, if n = 3, then if we pre-multiply B by A, we get 1711 AB=[\"11 \"12 \"13] 521 I731 =\"11b11+ \"12b21 + \"13b31 Note that dub\" + a12b21 + (1132:!\" is not a matrix, nor a vector, but is simply an ordinary number. In matrix algebra, an ordinary number is called a scalar. So, in general, if a column vector is pre-multiplied by a row vector, the result is a scalar. In contrast, if we post-multiply B by A we get 1'11 BA: I721 [allalz l\"13] 531 bllall bllalz bilals b31all 5315112 b31a13 In general, if a column vector is post-multiplied by a row vector, the result is a matrix