Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
-$$\left\{ \begin{aligned}
3 x + 9 y - z & = 53 \
x - 9 y + 9 z & = 11 \
- 4 x + y + z & = 5
\end{aligned} \right.$$
A) $x = 2 , y = 6 , z = 7$
B) $x = - 2 , y = 6 , z = 4$
C) $x = 2 , y = 7 , z = 6$
D) Inconsistent

Question

Quizplus · Accepted Answer

To solve the system of equations using matrices and row operations, we first write the augmented matrix corresponding to the system:$$\begin{align*}\left[\begin{array}{ccc|c}3 & 9 & -1 & 53 \1 & -9 & 9 & 11 \-4 & 1 & 1 & 5 \\end{array}\right]\end{align*}$$Then, we perform row operations to get it into reduced row echelon form (RREF).1. $R_2 = R_2 - \frac{1}{3}R_1$ to make the coefficient of $x$ in the second row 0.2. $R_3 = R_3 + 4R_1$ to make the coefficient of $x$ in the third row 0.3. Continue with similar operations to make the matrix upper triangular and then back substitute or continue to RREF.After performing the necessary row operations, we find the solution to be $x = 2$, $y = 6$, $z = 7$, which corresponds to option A. This process involves several steps of adding, subtracting, and multiplying rows by constants to isolate variables, which ultimately reveals the solution.

Solve Each System of Equations Using Matrices (Row Operations) {3x+9y−z=53x−9y+9z=11−4x+y+z=5\left\{ \begin{aligned}3 x + 9 y - z & = 53 \\x - 9 y + 9 z & = 11 \\- 4 x + y + z & = 5\end{aligned} \right.⎩⎨⎧​3x+9y−zx−9y+9z−4x+y+z​=53=11=5​

Solve Each System of Equations Using Matrices (Row Operations) $\left\{ \begin{aligned}3 x + 9 y - z & = 53 \\x - 9 y + 9 z & = 11 \\- 4 x + y + z & = 5\end{aligned} \right.$