लीनियर एलजेब्रा उदाहरण

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

चरण 1

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

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

चरण 1.2

$R_{1}$ को सरल करें.

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

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 $0$ .

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

चरण 2.2

$R_{2}$ को सरल करें.

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{4}{5} \\ 0 & - \frac{1}{5} & \frac{21}{5} \\ 0 & 1 & 1 \end{array}]$

चरण 3

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

और स्टेप्स के लिए टैप करें…

चरण 3.1

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

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{4}{5} \\ - 5 \cdot 0 & - 5 (- \frac{1}{5}) & - 5 (\frac{21}{5}) \\ 0 & 1 & 1 \end{array}]$

चरण 3.2

$R_{2}$ को सरल करें.

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{4}{5} \\ 0 & 1 & - 21 \\ 0 & 1 & 1 \end{array}]$

चरण 4

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 4.1

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

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{4}{5} \\ 0 & 1 & - 21 \\ 0 - 0 & 1 - 1 & 1 + 21 \end{array}]$

चरण 4.2

$R_{3}$ को सरल करें.

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{4}{5} \\ 0 & 1 & - 21 \\ 0 & 0 & 22 \end{array}]$

चरण 5

Multiply each element of $R_{3}$ by $\frac{1}{22}$ to make the entry at $3, 3$ a $1$ .

और स्टेप्स के लिए टैप करें…

चरण 5.1

Multiply each element of $R_{3}$ by $\frac{1}{22}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{4}{5} \\ 0 & 1 & - 21 \\ \frac{0}{22} & \frac{0}{22} & \frac{22}{22} \end{array}]$

चरण 5.2

$R_{3}$ को सरल करें.

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{4}{5} \\ 0 & 1 & - 21 \\ 0 & 0 & 1 \end{array}]$

चरण 6

Perform the row operation $R_{2} = R_{2} + 21 R_{3}$ to make the entry at $2, 3$ a $0$ .

और स्टेप्स के लिए टैप करें…

चरण 6.1

Perform the row operation $R_{2} = R_{2} + 21 R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & \frac{1}{5} & \frac{4}{5} \\ 0 + 21 \cdot 0 & 1 + 21 \cdot 0 & - 21 + 21 \cdot 1 \\ 0 & 0 & 1 \end{array}]$

चरण 6.2

$R_{2}$ को सरल करें.

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

चरण 7

Perform the row operation $R_{1} = R_{1} - \frac{4}{5} R_{3}$ to make the entry at $1, 3$ a $0$ .

और स्टेप्स के लिए टैप करें…

चरण 7.1

Perform the row operation $R_{1} = R_{1} - \frac{4}{5} R_{3}$ to make the entry at $1, 3$ a $0$ .

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

चरण 7.2

$R_{1}$ को सरल करें.

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

चरण 8

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

और स्टेप्स के लिए टैप करें…

चरण 8.1

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

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

चरण 8.2

$R_{1}$ को सरल करें.

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