Question

what is the row echelon form of this matrix?\
\\(\

$$\begin{bmatrix}2 & 4 & 6\\\\ -4 & 7 & 3\\\\ 4 & -1 & 2\\end{bmatrix}$$

\\)\
\
\\(\boldsymbol{\circ}\\) a. \\(\

$$\begin{bmatrix}1 & 2 & 3\\\\ 0 & 1 & 5\\\\ 0 & 0 & 1\\end{bmatrix}$$

\\)\
\\(\boldsymbol{\circ}\\) b. \\(\

$$\begin{bmatrix}1 & 2 & 3\\\\ 0 & 1 & 1\\\\ 0 & 0 & 1\\end{bmatrix}$$

\\)\
\\(\boldsymbol{\circ}\\) c. \\(\

$$\begin{bmatrix}1 & 2 & 3\\\\ 0 & 1 & 1\\\\ 0 & -9 & 10\\end{bmatrix}$$

\\)\
\\(\boldsymbol{\circ}\\) d. \\(\

$$\begin{bmatrix}1 & 2 & 3\\\\ 0 & 15 & 15\\\\ 4 & -1 & 2\\end{bmatrix}$$

\\)

Explanation:

Step1: Simplify Row 1

Divide Row 1 by 2:

$$R_1 = \frac{1}{2}R_1 \implies
LATEXBLOCK0
$$

Step2: Eliminate $R_2$ first element

Add $4R_1$ to Row 2:

$$R_2 = R_2 + 4R_1 \implies
LATEXBLOCK1
$$

Step3: Eliminate $R_3$ first element

Subtract $4R_1$ from Row 3:

$$R_3 = R_3 - 4R_1 \implies
LATEXBLOCK2
$$

Step4: Simplify Row 2

Divide Row 2 by 15:

$$R_2 = \frac{1}{15}R_2 \implies
LATEXBLOCK3
$$

Step5: Eliminate $R_3$ second element

Add $9R_2$ to Row 3:

$$R_3 = R_3 + 9R_2 \implies
LATEXBLOCK4
$$

Step6: Simplify Row 3 sign

Multiply Row 3 by -1:

$$R_3 = -R_3 \implies
LATEXBLOCK5
$$

Answer:

B.

$$\begin{bmatrix}1 & 2 & 3\\0 & 1 & 1\\0 & 0 & 1\end{bmatrix}$$