प्री-कैलकुलस उदाहरण

$2 x - 2 y + 3 z = 2$ , $2 x - 3 y + 7 z = - 1$ , $4 x - 3 y + 2 z = 0$

चरण 1

Write the system as a matrix.

$[\begin{array}{c} 2 & - 2 & 3 & 2 \\ 2 & - 3 & 7 & - 1 \\ 4 & - 3 & 2 & 0 \end{array}]$

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 $1$ .

$[\begin{array}{c} \frac{2}{2} & \frac{- 2}{2} & \frac{3}{2} & \frac{2}{2} \\ 2 & - 3 & 7 & - 1 \\ 4 & - 3 & 2 & 0 \end{array}]$

चरण 2.1.2

$R_{1}$ को सरल करें.

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ 2 & - 3 & 7 & - 1 \\ 4 & - 3 & 2 & 0 \end{array}]$

चरण 2.2

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

और स्टेप्स के लिए टैप करें…

चरण 2.2.1

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

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ 2 - 2 \cdot 1 & - 3 - 2 \cdot - 1 & 7 - 2 (\frac{3}{2}) & - 1 - 2 \cdot 1 \\ 4 & - 3 & 2 & 0 \end{array}]$

चरण 2.2.2

$R_{2}$ को सरल करें.

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ 0 & - 1 & 4 & - 3 \\ 4 & - 3 & 2 & 0 \end{array}]$

चरण 2.3

Perform the row operation $R_{3} = R_{3} - 4 R_{1}$ to make the entry at $3, 1$ a $0$ .

और स्टेप्स के लिए टैप करें…

चरण 2.3.1

Perform the row operation $R_{3} = R_{3} - 4 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ 0 & - 1 & 4 & - 3 \\ 4 - 4 \cdot 1 & - 3 - 4 \cdot - 1 & 2 - 4 (\frac{3}{2}) & 0 - 4 \cdot 1 \end{array}]$

चरण 2.3.2

$R_{3}$ को सरल करें.

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ 0 & - 1 & 4 & - 3 \\ 0 & 1 & - 4 & - 4 \end{array}]$

चरण 2.4

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

और स्टेप्स के लिए टैप करें…

चरण 2.4.1

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

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ - 0 & - - 1 & - 1 \cdot 4 & - - 3 \\ 0 & 1 & - 4 & - 4 \end{array}]$

चरण 2.4.2

$R_{2}$ को सरल करें.

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ 0 & 1 & - 4 & 3 \\ 0 & 1 & - 4 & - 4 \end{array}]$

चरण 2.5

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

और स्टेप्स के लिए टैप करें…

चरण 2.5.1

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

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ 0 & 1 & - 4 & 3 \\ 0 - 0 & 1 - 1 & - 4 + 4 & - 4 - 3 \end{array}]$

चरण 2.5.2

$R_{3}$ को सरल करें.

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ 0 & 1 & - 4 & 3 \\ 0 & 0 & 0 & - 7 \end{array}]$

चरण 2.6

Multiply each element of $R_{3}$ by $- \frac{1}{7}$ to make the entry at $3, 4$ a $1$ .

और स्टेप्स के लिए टैप करें…

चरण 2.6.1

Multiply each element of $R_{3}$ by $- \frac{1}{7}$ to make the entry at $3, 4$ a $1$ .

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ 0 & 1 & - 4 & 3 \\ - \frac{1}{7} \cdot 0 & - \frac{1}{7} \cdot 0 & - \frac{1}{7} \cdot 0 & - \frac{1}{7} \cdot - 7 \end{array}]$

चरण 2.6.2

$R_{3}$ को सरल करें.

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ 0 & 1 & - 4 & 3 \\ 0 & 0 & 0 & 1 \end{array}]$

चरण 2.7

Perform the row operation $R_{2} = R_{2} - 3 R_{3}$ to make the entry at $2, 4$ a $0$ .

और स्टेप्स के लिए टैप करें…

चरण 2.7.1

Perform the row operation $R_{2} = R_{2} - 3 R_{3}$ to make the entry at $2, 4$ a $0$ .

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ 0 - 3 \cdot 0 & 1 - 3 \cdot 0 & - 4 - 3 \cdot 0 & 3 - 3 \cdot 1 \\ 0 & 0 & 0 & 1 \end{array}]$

चरण 2.7.2

$R_{2}$ को सरल करें.

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 1 \\ 0 & 1 & - 4 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$

चरण 2.8

Perform the row operation $R_{1} = R_{1} - R_{3}$ to make the entry at $1, 4$ a $0$ .

और स्टेप्स के लिए टैप करें…

चरण 2.8.1

Perform the row operation $R_{1} = R_{1} - R_{3}$ to make the entry at $1, 4$ a $0$ .

$[\begin{array}{c} 1 - 0 & - 1 - 0 & \frac{3}{2} - 0 & 1 - 1 \\ 0 & 1 & - 4 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$

चरण 2.8.2

$R_{1}$ को सरल करें.

$[\begin{array}{c} 1 & - 1 & \frac{3}{2} & 0 \\ 0 & 1 & - 4 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$

चरण 2.9

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

और स्टेप्स के लिए टैप करें…

चरण 2.9.1

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

$[\begin{array}{c} 1 + 0 & - 1 + 1 \cdot 1 & \frac{3}{2} - 4 & 0 + 0 \\ 0 & 1 & - 4 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$

चरण 2.9.2

$R_{1}$ को सरल करें.

$[\begin{array}{c} 1 & 0 & - \frac{5}{2} & 0 \\ 0 & 1 & - 4 & 0 \\ 0 & 0 & 0 & 1 \end{array}]$

चरण 3

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

$x - \frac{5}{2} z = 0$

$y - 4 z = 0$

$0 = 1$

चरण 4

The system is inconsistent so there is no solution.

$कोई हल नहीं$