Matrix Problem

[zeamju]

I need some help multiplying matrices. I already know the answer but I need to understand how the problem was solved for future reference. The problem was to multiply an inverse matrix by a column matrix:

The inverse matrix is 2 x 2. The first row first column is -(5/17). Row one column two is (9/17).

Row Two column one is (3/17). Row two column two is -(2/17).

The column matrix is 2104 and 1541. I know the answer is 197 at the top and 190 at the bottom. Need some help figuring out how to arrive at that answer? Any help would be greatly appreciated.

 

[tkhunny]

Have you tried the rules of matrix multiplication?

(1/17) * [(-5*2104)+(9*1541)]

(1/17) * [(3*2104)+(-2*1541)]

 

[Deleted member 4993]

I need some help multiplying matrices. I already know the answer but I need to understand how the problem was solved for future reference. The problem was to multiply an inverse matrix by a column matrix:

The inverse matrix is 2 x 2. The first row first column is -(5/17). Row one column two is (9/17).

Row Two column one is (3/17). Row two column two is -(2/17).

The column matrix is 2104 and 1541. I know the answer is 197 at the top and 190 at the bottom. Need some help figuring out how to arrive at that answer? Any help would be greatly appreciated.

|a  b| |e|
|c  d| |f|

equals to

|(a*e + b*f)|
|(c*e + d*f)|

 

[galactus]

Matrices can be set up in LaTeX by using \begin{bmatrix} \end{bmatrix}

\(\displaystyle \begin{bmatrix}\frac{-5}{17}&\frac{9}{17}\\ \;\ & \;\ \\ \frac{3}{17}&\frac{-2}{17}\end{bmatrix}\cdot \begin{bmatrix}2104\\ \;\ \\ 1541\end{bmatrix}=\begin{bmatrix}\frac{-5}{17}\cdot 2104+\frac{9}{17}\cdot 1541\\ \;\ \\ \frac{3}{17}\cdot 2104+\frac{-2}{17}\cdot 1541\end{bmatrix}=\begin{bmatrix}197\\ \;\ \\190\end{bmatrix}\)

 

[zeamju]

Thank you for all you help! I wish my textbook could have explained it as easily you have!