- #1
Saladsamurai
- 3,020
- 7
Problem Statement
Let
[tex]\mathbf{y} = [y_1\, y_2\, ...\, y_m][/tex]
And
[tex]A =
\left[\begin{array} {cccc}
a_{11}&a_{12}&...&a_{1n}\\
a_{21}&a_{22}&...&a_{2n}\\
a_{m1}&a_{m2}&...&a_{mn}
\end{array}\right]
[/tex]
Show that the product yA can be expressed as a linear combination of the row matrices of A
with the scalar coefficients coming from y
Attempt at Solution
I thought that I would write out the actual product, which is a row vector. I thought that
something might jump out at me from here:
yA = [(y1a11 + y2a21 + ... + ymam1) (y1a12 + y2a22 + ... + ymam2) (y1a1n + y2a2n + ... + ymamn)]
I am not sure where to go from here. I know that it is going to be a summation of the rows of A ... but what I have now is just written column-wise... and it is not a summation.
A hint maybe?
Let
[tex]\mathbf{y} = [y_1\, y_2\, ...\, y_m][/tex]
And
[tex]A =
\left[\begin{array} {cccc}
a_{11}&a_{12}&...&a_{1n}\\
a_{21}&a_{22}&...&a_{2n}\\
a_{m1}&a_{m2}&...&a_{mn}
\end{array}\right]
[/tex]
Show that the product yA can be expressed as a linear combination of the row matrices of A
with the scalar coefficients coming from y
Attempt at Solution
I thought that I would write out the actual product, which is a row vector. I thought that
something might jump out at me from here:
yA = [(y1a11 + y2a21 + ... + ymam1) (y1a12 + y2a22 + ... + ymam2) (y1a1n + y2a2n + ... + ymamn)]
I am not sure where to go from here. I know that it is going to be a summation of the rows of A ... but what I have now is just written column-wise... and it is not a summation.
A hint maybe?