Question

I need a little bit of help on question 19, Thanks!

Answer 1

We are given the following matrix:

`\begin{bmatrix}{1} & {-3} & {4\parallel} & {3} \\ {2} & {-5} & {6\parallel} & {6} \\ {-3} & {3} & {4\parallel} & {6} \\ {} & {} & {} & {}\end{bmatrix}`

We are asked to do the following operation:

`R_2=-2r_1+r_2`

Here:

`r_1,r_2`

Represent rows 1 and 2 respectively. Therefore, the operation asks us to multiply row 1 by -2 and add the result to row 2. Therefore, we need to multiply each element of the first row by -2 and add that to the element in the same column of the second row.

Let's take the first element of the first row, we will mutiliply it by -2 and add that to the first element of the second row:

`(-2)(1)+2=-2+2=0`

This will be the new element in the second row. Another example, let's take the second element of the first row then add the result to the second element of the second row:

`(-2)(-3)-5=6-5=1`

Therefore, this is the new second element of the second row. Continuing with this procedure we replace all the elements of the second row according to the results of the operations and we get the new matrix:

`\begin{bmatrix}{1} & {-3} & {4\parallel} & {3} \\ {0} & {1} & {-2\parallel} & {0} \\ {-3} & {3} & {4\parallel} & {6} \\ {} & {} & {} & {}\end{bmatrix}`

And thus we have performed the operation on the matrix.