Why is it that when multiplying a (1x3) by (3x1) matrix, you get a (1x1) matrix, but when multiplying a (3x1) matrix by a (1x3) matrix, you get a (3x3) matrix? Why is matrix multiplication defined this way?

Oct 25, 2022 · As a beginner think of 1x3 matrix as three one-dimensional vectors and 3x1 matrix as one three-dimensional vector. In order to understand the difference between the products, consider …

Oct 14, 2014 · If you multiplied the matrices in the reverse order, you'd get a $1 \times 1$ matrix $ {\bf b}^\top {\bf a}$, with sole entry $$\sum_ {i = 1}^3 a_i b_i,$$ which is just the inner product of $ {\bf a}, …

Oct 17, 2016 · Matrix multiplication question of 2 3x1 vectors Ask Question Asked 9 years, 1 month ago Modified 9 years, 1 month ago

2 I have 2 matrices and have been trying to multiply them but to no avail. Then I found this online site and trying feeding it the values but yet no success. - R' . T is what i would like to do but R is a 3x3 (3 …

Notice that a set of two vector is linearly independent iff neither vector is a multiple of the other, and a set consisting of one vector is linearly independent iff the vector is nonzero. (Also, your statement …

Apr 24, 2020 · Since the cross product of two 3x1 vectors is a 3x1 vector, would we by analogy say that the cross product of two 3x3 matrices would be a 3x3x3 matrix? And would we calculate the third …

Jul 13, 2022 · 3. BTW, get rid of the notion that the directed line segment (i.e., arrow) is the real vector and that that 3x1 matrix (i.e., column vector) is just its representation; a vector is an abstract object …

Jun 11, 2017 · I'm a newbie of Matlab and non-native English language. I have question what is inverse of matrix (3*1) such as 1 2 3 I got an answer matrix (1*3) [1/14, 2/14, 3/14] by Matlab Can you help …

Jun 20, 2016 · I would think the span of a single vector is simply the line it makes within it's $d$-dimensional space (in this case $3$).