Use the given row transformation to change each matrix as indicat...

Question

Use the given row transformation to change each matrix as indicated. See Sample 1. 
< 2x2 Matrix > ; -7 times row 1 added to row 2

Accepted Answer

Hello, everyone. We are asked to apply the indicated row transformation to the following matrix. We are given a two by two matrix where the first row is six negative nine. And the second row is 11 0, we are asked to add the result negative 10 times row one to row two. We have four answer choices all of which are two by two matrices with slightly different answers in them. So thinking about what add the result negative 10 times of row one to row two means this means we're gonna do negative 10 multiplied by the element from row one. And then we're gonna add it to the element from row two. So in doing so row one does not change. So it remains six negative nine. However, in row two, we need to do negative 10 multiplied by the corresponding value from row one to the first element of row one, which is six. And then we're gonna add the element from row two in our original matrix which is 11. Same thing with the second element for row two. We're gonna do negative 10 multiplied by the element in the second spot in row one. Which is negative nine and add the element that is originally in row two, which is zero. So now doing out the multiplication in addition, again, row one is not changing. It is still six negative nine row two. The first element negative 10 multiplied by six is negative 60 negative 60 plus 11 is negative 49. And in the second element of row two, negative 10 multiplied by negative nine is positive 90 plus zero is still positive 90. So our answer is a two by two matrix where the top row is six negative nine. And the second row is negative 49 90. And this matches answer choice A have a nice day.

Use the given row transformation to change each matrix as indicated. See Sample 1. < 2x2 Matrix > ; -7 times row 1 added to row 2