QuestionRow reduce the matrix and find pivot positions. Given matrix: $\left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 6 & 7 & 8 & 9 \end{array}\right]$

Studdy Solution

STEP 1

Assumptions1. The given matrix is a3x4 matrix. . We need to row reduce this matrix to its reduced echelon form.
3. We need to identify the pivot positions in the final matrix and in the original matrix.

STEP 2

We start by subtracting5 times the first row from the second row and6 times the first row from the third row to eliminate the leading coefficients in the second and third rows.
$\left[\begin{array}{cccc} 1 &2 & &4 \\ 0 & -4 & -8 & -12 \\ 0 & -5 & -10 & -15\end{array}\right]$

STEP 3

Next, we divide the second row by - and the third row by -5 to make the leading coefficient of the second and third rows equal to1.
$\left[\begin{array}{cccc} 1 &2 &3 & \\ 0 &1 &2 &3 \\ 0 &1 &2 &3\end{array}\right]$

STEP 4

Now, we subtract the second row from the third row to eliminate the leading coefficient in the third row.
$\left[\begin{array}{cccc} 1 &2 &3 &4 \\ 0 &1 &2 &3 \\ 0 &0 &0 &0\end{array}\right]$

STEP 5

Finally, we subtract2 times the second row from the first row to eliminate the second coefficient in the first row.
$\left[\begin{array}{cccc} 1 &0 & -1 & -2 \\ 0 &1 &2 &3 \\ 0 &0 &0 &0\end{array}\right]$ This is the reduced echelon form of the given matrix. The pivot positions in the final matrix are the first elements in the first and second rows, so the correct answer for the final matrix is not provided in the options.

STEP 6

The pivot positions in the original matrix are the first elements in the first, second, and third rows. So, the correct answer for the original matrix is also not provided in the options.

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QuestionRow reduce the matrix and find pivot positions. Given matrix: $\left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 6 & 7 & 8 & 9 \end{array}\right]$

Studdy Solution

STEP 1

Assumptions1. The given matrix is a3x4 matrix. . We need to row reduce this matrix to its reduced echelon form.
3. We need to identify the pivot positions in the final matrix and in the original matrix.

STEP 2

We start by subtracting5 times the first row from the second row and6 times the first row from the third row to eliminate the leading coefficients in the second and third rows.
$\left[\begin{array}{cccc} 1 &2 & &4 \\ 0 & -4 & -8 & -12 \\ 0 & -5 & -10 & -15\end{array}\right]$

STEP 3

Next, we divide the second row by - and the third row by -5 to make the leading coefficient of the second and third rows equal to1.
$\left[\begin{array}{cccc} 1 &2 &3 & \\ 0 &1 &2 &3 \\ 0 &1 &2 &3\end{array}\right]$

STEP 4

Now, we subtract the second row from the third row to eliminate the leading coefficient in the third row.
$\left[\begin{array}{cccc} 1 &2 &3 &4 \\ 0 &1 &2 &3 \\ 0 &0 &0 &0\end{array}\right]$

STEP 5

STEP 6

The pivot positions in the original matrix are the first elements in the first, second, and third rows. So, the correct answer for the original matrix is also not provided in the options.

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QuestionRow reduce the matrix and find pivot positions. Given matrix: [123456786789] \left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 6 & 7 & 8 & 9 \end{array}\right] ⎣⎡​156​267​378​489​⎦⎤​

Studdy Solution

STEP 1

Assumptions1. The given matrix is a3x4 matrix. . We need to row reduce this matrix to its reduced echelon form.3. We need to identify the pivot positions in the final matrix and in the original matrix.

STEP 2

STEP 3

Next, we divide the second row by - and the third row by -5 to make the leading coefficient of the second and third rows equal to1.[12301230123]\left[\begin{array}{cccc} 1 &2 &3 & \\ 0 &1 &2 &3 \\ 0 &1 &2 &3\end{array}\right] ⎣⎡​100​211​322​33​⎦⎤​

STEP 4

Now, we subtract the second row from the third row to eliminate the leading coefficient in the third row.[123401230000]\left[\begin{array}{cccc} 1 &2 &3 &4 \\ 0 &1 &2 &3 \\ 0 &0 &0 &0\end{array}\right] ⎣⎡​100​210​320​430​⎦⎤​

STEP 5

STEP 6

The pivot positions in the original matrix are the first elements in the first, second, and third rows. So, the correct answer for the original matrix is also not provided in the options.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionRow reduce the matrix and find pivot positions. Given matrix: $\left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 6 & 7 & 8 & 9 \end{array}\right]$

Assumptions1. The given matrix is a3x4 matrix. . We need to row reduce this matrix to its reduced echelon form.
3. We need to identify the pivot positions in the final matrix and in the original matrix.

Next, we divide the second row by - and the third row by -5 to make the leading coefficient of the second and third rows equal to1.
$\left[\begin{array}{cccc} 1 &2 &3 & \\ 0 &1 &2 &3 \\ 0 &1 &2 &3\end{array}\right]$

Now, we subtract the second row from the third row to eliminate the leading coefficient in the third row.
$\left[\begin{array}{cccc} 1 &2 &3 &4 \\ 0 &1 &2 &3 \\ 0 &0 &0 &0\end{array}\right]$