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

Question

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

$[\begin{matrix} 1 & 5 & 6 \\ - 4 & - 1 & 2 \\ 3 & 7 & 1 \end{matrix}],$

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 where the top row is 582. The second row is negative 10, negative 53. The third row is 465. And we are asked to add the result eight times of row one to row two. We are given four answer choices all of which are three by three matrices. They all vary slightly in terms of sign and value. Adding the result eight times of row one to row two means we are multiplying row one by eight and adding that value to the value already in row two. So when we draw this out, the values in row one actually do not change. So they stay 582 in row two, we are gonna do eight times the element in that spot from row one. So eight times 10 for the first element of the second row. And we're gonna add that to the element that's already there, which is negative 10. For the second element of the second row, we do eight times the value from row one which is eight plus the value from row two, which is negative five. And for the third element, we do eight multiplied by the value from row one, which is two added to the value from row two, which is three, row three does not change, it stays 465. Nothing changes in row three. Now, we need to do the multiplication and addition in row two to find our final answer again. Row one remains in row 28, multiplied by five is 40 plus negative 10 is 30. For the second element eight multiplied by eight is plus negative five is 59. And for the third element eight multiplied by two is 16 plus three is 19. And the bottom row did not change 465. So our solution matrix is the three by three matrix with the top row as 582, the second row as 30 59 19, third row as 465. And that looks like it matches answer choice B have a nice day.

Use the given row transformation to change each matrix as indicated.
$[\begin{matrix} 1 & 5 & 6 \\ - 4 & - 1 & 2 \\ 3 & 7 & 1 \end{matrix}],$

Key Concepts

Elementary Row Operations

Matrix Representation and Notation

Row Addition Operation

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