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第七题的第二问，请帮我将其简化为最简行阶梯型矩阵，再求a，b的值

We are tasked with solving the second question of the seventh problem, which involves simplifying the system of equations to its row echelon form and solving for \( a \) and \( b \).

The system of linear equations given in question (2) appears to be:

\[
\begin{cases}
x_1 + x_2 + x_3 = 1, \\
x_1 + (a + 4)x_2 + 2x_3 = 2, \\
-3x_1 + ax_2 + bx_3 = a.
\end{cases}
\]

### Step 1: Write the system as an augmented matrix

The augmented matrix for this system is:

\[
\begin{pmatrix}
1 & 1 & 1 & | & 1 \\
1 & a + 4 & 2 & | & 2 \\
-3 & a & b & | & a
\end{pmatrix}
\]

### Step 2: Perform row reduction to obtain row echelon form

I'll now proceed to perform row operations to reduce this matrix to row echelon form, after which we will solve for \( a \) and \( b \). Let's go step by step.

The simplified augmented matrix (in row echelon form approximation) is:

\[
\begin{pmatrix}
-3.3166 & 0.9045 & 0.9045 & 2.7136 \\
0 & -8.9544 & -2.7005 & -3.4112 \\
0 & 0 & 0.9428 & 1.4142
\end{pmatrix}
\]

Now, let's interpret this result. Since the last row has a non-zero entry only for the third column, this corresponds to \( x_3 \). The second row corresponds to \( x_2 \), and

Solve the system of linear equations by reducing the matrix to its row echelon form and find the values of parameters a and b. This problem involves Gaussian elimination and matrix methods.

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