Question

Given the following matrices, what 3 elements make up the first column of the product matrix DA?

Answer 1

We have to figure out what the product of DA is,

$\begin{bmatrix}-1&2&3\\8&-4&0\\6&7&1\\ \end{bmatrix}\begin{bmatrix}1\\3\\5\\ \end{bmatrix}=\begin{bmatrix}a\\b\\c\\ \end{bmatrix}$

We know that,

$\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\\\end{bmatrix}\begin{bmatrix}x\\y\\z\\\end{bmatrix}=\begin{bmatrix}ax+by+cz\\dx+ey+fz\\gx+hy+iz\\\end{bmatrix}$

So,

$a=-1\cdot1+2\cdot3+3\cdot5=-1+6+15=20$

$b=8\cdot1+(-4)\cdot3+0\cdot5=8-12=-4$

$c=6\cdot1+7\cdot3+1\cdot5=6+21+5=32$

So the solution is,

$a,b,c=\boxed{20,-4,32}$

Hope this helps :)