Question

Help me pleaseeeee :(

Answer 1

I'm taking linear algebra right now so this one hits home :)

Elementary Row Operations (EROs) are very important and not too difficult, so let's dive into the problem!

You're given the matrix below and asked to perform a single ERO to produce a matrix with a 1 at the position (1,1):

`\begin{bmatrix}3 & 10 & 5\\2 & -1 & 1\end{bmatrix}`

Think of the two rows as separate entities in the matrix. Ultimately we want to have the index (1,1) currently holding the number 3 to become the number 1. To do this, logically you just need to subtract 2. Now, looking at the rows we have, a simple row operation is quite apparent.

Simply subtract row 2 from row 1, shown below:

`\begin{bmatrix}3-2 & 10-(-1) & 5-1\\2 & -1 & 1\end{bmatrix}`

Now, simplify and you will have the answer:

`\begin{bmatrix}1 & 11 & 4\\2 & -1 & 1\end{bmatrix}`

Notice that our matrix now has the required number 1 in row 1 and column 1, therefore, the matrix above is our answer! Let me know if you have any questions!