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Math  /  Algebra

QuestionWhat row operation will transform [−4−7−27−4610−187−1−7−5] into [−4−7−27−235−97−1−7−5]\left[\begin{array}{cccc} -4 & -7 & -2 & 7 \\ -4 & 6 & 10 & -18 \\ 7 & -1 & -7 & -5 \end{array}\right] \text { into }\left[\begin{array}{cccc} -4 & -7 & -2 & 7 \\ -2 & 3 & 5 & -9 \\ 7 & -1 & -7 & -5 \end{array}\right] □\square Select an answer ∘→\circ \rightarrow Select an answer 0

Studdy Solution

STEP 1

1. We are given two matrices and need to determine the row operation that transforms the first matrix into the second.
2. The matrices have the same number of rows and columns.

STEP 2

1. Identify the rows that differ between the two matrices.
2. Determine the row operation needed to transform the differing row in the first matrix to match the second matrix.

STEP 3

Compare each row of the two matrices to identify which rows are different.
- Row 1: [−4,−7,−2,7][-4, -7, -2, 7] is the same in both matrices. - Row 2: [−4,6,10,−18][-4, 6, 10, -18] in the first matrix and [−2,3,5,−9][-2, 3, 5, -9] in the second matrix. - Row 3: [7,−1,−7,−5][7, -1, -7, -5] is the same in both matrices.
The differing row is Row 2.

STEP 4

Determine the row operation needed to transform Row 2 of the first matrix into Row 2 of the second matrix.
- The first element of Row 2 changes from −4-4 to −2-2. - The second element changes from 66 to 33. - The third element changes from 1010 to 55. - The fourth element changes from −18-18 to −9-9.
Notice that each element in Row 2 of the second matrix is half of the corresponding element in Row 2 of the first matrix.
The row operation is to multiply Row 2 by 12\frac{1}{2}.
The row operation that transforms the first matrix into the second matrix is:
Multiply Row 2 by 12\frac{1}{2}.

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