लीनियर एलजेब्रा उदाहरण

$[\begin{array}{c} 2 & 5 & 1 \\ - 1 & 0 & 1 \\ 3 & 4 & - 1 \end{array}]$

चरण 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 1.1

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

$[\begin{array}{c} \frac{2}{2} & \frac{5}{2} & \frac{1}{2} \\ - 1 & 0 & 1 \\ 3 & 4 & - 1 \end{array}]$

चरण 1.2

$R_{1}$ को सरल करें.

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{1}{2} \\ - 1 & 0 & 1 \\ 3 & 4 & - 1 \end{array}]$

चरण 2

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

और स्टेप्स के लिए टैप करें…

चरण 2.1

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

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{1}{2} \\ - 1 + 1 \cdot 1 & 0 + \frac{5}{2} & 1 + \frac{1}{2} \\ 3 & 4 & - 1 \end{array}]$

चरण 2.2

$R_{2}$ को सरल करें.

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{1}{2} \\ 0 & \frac{5}{2} & \frac{3}{2} \\ 3 & 4 & - 1 \end{array}]$

चरण 3

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

और स्टेप्स के लिए टैप करें…

चरण 3.1

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

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{1}{2} \\ 0 & \frac{5}{2} & \frac{3}{2} \\ 3 - 3 \cdot 1 & 4 - 3 (\frac{5}{2}) & - 1 - 3 (\frac{1}{2}) \end{array}]$

चरण 3.2

$R_{3}$ को सरल करें.

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{1}{2} \\ 0 & \frac{5}{2} & \frac{3}{2} \\ 0 & - \frac{7}{2} & - \frac{5}{2} \end{array}]$

चरण 4

Multiply each element of $R_{2}$ by $\frac{2}{5}$ to make the entry at $2, 2$ a $1$ .

और स्टेप्स के लिए टैप करें…

चरण 4.1

Multiply each element of $R_{2}$ by $\frac{2}{5}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{1}{2} \\ \frac{2}{5} \cdot 0 & \frac{2}{5} \cdot \frac{5}{2} & \frac{2}{5} \cdot \frac{3}{2} \\ 0 & - \frac{7}{2} & - \frac{5}{2} \end{array}]$

चरण 4.2

$R_{2}$ को सरल करें.

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{1}{2} \\ 0 & 1 & \frac{3}{5} \\ 0 & - \frac{7}{2} & - \frac{5}{2} \end{array}]$

चरण 5

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

और स्टेप्स के लिए टैप करें…

चरण 5.1

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

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{1}{2} \\ 0 & 1 & \frac{3}{5} \\ 0 + \frac{7}{2} \cdot 0 & - \frac{7}{2} + \frac{7}{2} \cdot 1 & - \frac{5}{2} + \frac{7}{2} \cdot \frac{3}{5} \end{array}]$

चरण 5.2

$R_{3}$ को सरल करें.

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{1}{2} \\ 0 & 1 & \frac{3}{5} \\ 0 & 0 & - \frac{2}{5} \end{array}]$

चरण 6

Multiply each element of $R_{3}$ by $- \frac{5}{2}$ to make the entry at $3, 3$ a $1$ .

और स्टेप्स के लिए टैप करें…

चरण 6.1

Multiply each element of $R_{3}$ by $- \frac{5}{2}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{1}{2} \\ 0 & 1 & \frac{3}{5} \\ - \frac{5}{2} \cdot 0 & - \frac{5}{2} \cdot 0 & - \frac{5}{2} (- \frac{2}{5}) \end{array}]$

चरण 6.2

$R_{3}$ को सरल करें.

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{1}{2} \\ 0 & 1 & \frac{3}{5} \\ 0 & 0 & 1 \end{array}]$

चरण 7

Perform the row operation $R_{2} = R_{2} - \frac{3}{5} R_{3}$ to make the entry at $2, 3$ a $0$ .

और स्टेप्स के लिए टैप करें…

चरण 7.1

Perform the row operation $R_{2} = R_{2} - \frac{3}{5} R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & \frac{5}{2} & \frac{1}{2} \\ 0 - \frac{3}{5} \cdot 0 & 1 - \frac{3}{5} \cdot 0 & \frac{3}{5} - \frac{3}{5} \cdot 1 \\ 0 & 0 & 1 \end{array}]$

चरण 7.2

$R_{2}$ को सरल करें.

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

चरण 8

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

और स्टेप्स के लिए टैप करें…

चरण 8.1

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

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

चरण 8.2

$R_{1}$ को सरल करें.

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

चरण 9

Perform the row operation $R_{1} = R_{1} - \frac{5}{2} R_{2}$ to make the entry at $1, 2$ a $0$ .

और स्टेप्स के लिए टैप करें…

चरण 9.1

Perform the row operation $R_{1} = R_{1} - \frac{5}{2} R_{2}$ to make the entry at $1, 2$ a $0$ .

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

चरण 9.2

$R_{1}$ को सरल करें.

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