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. 
< 3x3 Matrix > ; 2 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 three by three matrix with the first row being 875. The second row is negative 31 negative eight. The third row is 12, 11 0. We are asked to add the result six times of row one to row two. We are given four answer choices all of which are three by three matrices with slightly varying values. Let's analyze what add the result six times of row one to row two means this means we are gonna take the value that is the element of row one multiply it by six and then add the element from row two. So when we do this, we will still result with a three by three matrix, the top row will not change. So 875, our second row, we're gonna take six and multiply it by the corresponding spot in the first row. So eight plus the value that was in row two before we did the transformation, which is negative three for the first element. For the second element. Again, we're gonna do six this time multiplied by seven because that is the second element in the first row. And we're gonna add it to the second element from the second row, which is one. And then for the third element, we do six multiplied by the third element of the first row, which is five plus the third element of the second row, which is negative eight. Our third row does not change. It is still 12, 11 0. So cleaning up the multiplication. In addition, we have a three by three matrix. Again, the top row is still 875. The second row we have times eight which is 48 plus three is 45. I'm sorry. Plus negative three is 45. The second element six multiplied by seven is 42 plus one is 43. And the third element six multiplied by five is plus negative eight is 22. The third row remains 12 11 0. So our answer is a three by three matrix where the first row is 875. The second row is 45 43 22. The third row is 12 11 0 and this matches answer choice C have a nice day.

Use the given row transformation to change each matrix as indicated. See Sample 1. < 3x3 Matrix > ; 2 times row 1 added to row 2

Key Concepts

Matrix Operations

Row Transformation

Scalar Multiplication

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