फाइनाइट मैथ उदाहरण

$- 2 x + 2 z = - 2$ , $6 y + 6 z = 84$ , $- 2 x + 7 y + 4 z = 56$

चरण 1

Write the system as a matrix.

$[\begin{array}{c} - 2 & 0 & 2 & - 2 \\ 0 & 6 & 6 & 84 \\ - 2 & 7 & 4 & 56 \end{array}]$

चरण 2

घटी हुई पंक्ति के सोपानक रूप का पता करें.

और स्टेप्स के लिए टैप करें…

चरण 2.1

Multiply each element of $R_{1}$ by $- \frac{1}{2}$ to make the entry at $1, 1$ a $1$ .

और स्टेप्स के लिए टैप करें…

चरण 2.1.1

Multiply each element of $R_{1}$ by $- \frac{1}{2}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} - \frac{1}{2} \cdot - 2 & - \frac{1}{2} \cdot 0 & - \frac{1}{2} \cdot 2 & - \frac{1}{2} \cdot - 2 \\ 0 & 6 & 6 & 84 \\ - 2 & 7 & 4 & 56 \end{array}]$

चरण 2.1.2

$R_{1}$ को सरल करें.

$[\begin{array}{c} 1 & 0 & - 1 & 1 \\ 0 & 6 & 6 & 84 \\ - 2 & 7 & 4 & 56 \end{array}]$

चरण 2.2

Perform the row operation $R_{3} = R_{3} + 2 R_{1}$ to make the entry at $3, 1$ a $0$ .

और स्टेप्स के लिए टैप करें…

चरण 2.2.1

Perform the row operation $R_{3} = R_{3} + 2 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & 0 & - 1 & 1 \\ 0 & 6 & 6 & 84 \\ - 2 + 2 \cdot 1 & 7 + 2 \cdot 0 & 4 + 2 \cdot - 1 & 56 + 2 \cdot 1 \end{array}]$

चरण 2.2.2

$R_{3}$ को सरल करें.

$[\begin{array}{c} 1 & 0 & - 1 & 1 \\ 0 & 6 & 6 & 84 \\ 0 & 7 & 2 & 58 \end{array}]$

चरण 2.3

Multiply each element of $R_{2}$ by $\frac{1}{6}$ to make the entry at $2, 2$ a $1$ .

और स्टेप्स के लिए टैप करें…

चरण 2.3.1

Multiply each element of $R_{2}$ by $\frac{1}{6}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 0 & - 1 & 1 \\ \frac{0}{6} & \frac{6}{6} & \frac{6}{6} & \frac{84}{6} \\ 0 & 7 & 2 & 58 \end{array}]$

चरण 2.3.2

$R_{2}$ को सरल करें.

$[\begin{array}{c} 1 & 0 & - 1 & 1 \\ 0 & 1 & 1 & 14 \\ 0 & 7 & 2 & 58 \end{array}]$

चरण 2.4

Perform the row operation $R_{3} = R_{3} - 7 R_{2}$ to make the entry at $3, 2$ a $0$ .

और स्टेप्स के लिए टैप करें…

चरण 2.4.1

Perform the row operation $R_{3} = R_{3} - 7 R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & 0 & - 1 & 1 \\ 0 & 1 & 1 & 14 \\ 0 - 7 \cdot 0 & 7 - 7 \cdot 1 & 2 - 7 \cdot 1 & 58 - 7 \cdot 14 \end{array}]$

चरण 2.4.2

$R_{3}$ को सरल करें.

$[\begin{array}{c} 1 & 0 & - 1 & 1 \\ 0 & 1 & 1 & 14 \\ 0 & 0 & - 5 & - 40 \end{array}]$

चरण 2.5

Multiply each element of $R_{3}$ by $- \frac{1}{5}$ to make the entry at $3, 3$ a $1$ .

और स्टेप्स के लिए टैप करें…

चरण 2.5.1

Multiply each element of $R_{3}$ by $- \frac{1}{5}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & 0 & - 1 & 1 \\ 0 & 1 & 1 & 14 \\ - \frac{1}{5} \cdot 0 & - \frac{1}{5} \cdot 0 & - \frac{1}{5} \cdot - 5 & - \frac{1}{5} \cdot - 40 \end{array}]$

चरण 2.5.2

$R_{3}$ को सरल करें.

$[\begin{array}{c} 1 & 0 & - 1 & 1 \\ 0 & 1 & 1 & 14 \\ 0 & 0 & 1 & 8 \end{array}]$

चरण 2.6

Perform the row operation $R_{2} = R_{2} - R_{3}$ to make the entry at $2, 3$ a $0$ .

और स्टेप्स के लिए टैप करें…

चरण 2.6.1

Perform the row operation $R_{2} = R_{2} - R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & 0 & - 1 & 1 \\ 0 - 0 & 1 - 0 & 1 - 1 & 14 - 8 \\ 0 & 0 & 1 & 8 \end{array}]$

चरण 2.6.2

$R_{2}$ को सरल करें.

$[\begin{array}{c} 1 & 0 & - 1 & 1 \\ 0 & 1 & 0 & 6 \\ 0 & 0 & 1 & 8 \end{array}]$

चरण 2.7

Perform the row operation $R_{1} = R_{1} + R_{3}$ to make the entry at $1, 3$ a $0$ .

और स्टेप्स के लिए टैप करें…

चरण 2.7.1

Perform the row operation $R_{1} = R_{1} + R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 + 0 & 0 + 0 & - 1 + 1 \cdot 1 & 1 + 1 \cdot 8 \\ 0 & 1 & 0 & 6 \\ 0 & 0 & 1 & 8 \end{array}]$

चरण 2.7.2

$R_{1}$ को सरल करें.

$[\begin{array}{c} 1 & 0 & 0 & 9 \\ 0 & 1 & 0 & 6 \\ 0 & 0 & 1 & 8 \end{array}]$

चरण 3

Use the result matrix to declare the final solution to the system of equations.

$x = 9$

$y = 6$

$z = 8$

चरण 4

The solution is the set of ordered pairs that make the system true.

$(9, 6, 8)$