लीनियर एलजेब्रा उदाहरण

$[\begin{array}{c} a - b & b + c \\ - 3 d + c & 2 a - 4 d \end{array}]$

चरण 1

घटी हुई पंक्ति के सोपानक रूप का पता करें.

और स्टेप्स के लिए टैप करें…

चरण 1.1

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

और स्टेप्स के लिए टैप करें…

चरण 1.1.1

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

$[\begin{array}{c} \frac{a - b}{a - b} & \frac{b + c}{a - b} \\ - 3 d + c & 2 a - 4 d \end{array}]$

चरण 1.1.2

$R_{1}$ को सरल करें.

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

चरण 1.2

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

और स्टेप्स के लिए टैप करें…

चरण 1.2.1

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

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

चरण 1.2.2

$R_{2}$ को सरल करें.

$[\begin{array}{c} 1 & \frac{b + c}{a - b} \\ 0 & - \frac{4 d a - 2 a^{2} + 2 a b - 7 d b - 3 d c + c b + c^{2}}{a - b} \end{array}]$

चरण 1.3

Multiply each element of $R_{2}$ by $- \frac{a - b}{4 d a - 2 a^{2} + 2 a b - 7 d b - 3 d c + c b + c^{2}}$ to make the entry at $2, 2$ a $1$ .

और स्टेप्स के लिए टैप करें…

चरण 1.3.1

Multiply each element of $R_{2}$ by $- \frac{a - b}{4 d a - 2 a^{2} + 2 a b - 7 d b - 3 d c + c b + c^{2}}$ to make the entry at $2, 2$ a $1$ .

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

चरण 1.3.2

$R_{2}$ को सरल करें.

$[\begin{array}{c} 1 & \frac{b + c}{a - b} \\ 0 & 1 \end{array}]$

चरण 1.4

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

और स्टेप्स के लिए टैप करें…

चरण 1.4.1

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

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

चरण 1.4.2

$R_{1}$ को सरल करें.

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

चरण 2

The pivot positions are the locations with the leading $1$ in each row. The pivot columns are the columns that have a pivot position.

Pivot Positions: $a_{11}$ and $a_{22}$

Pivot Columns: $1$ and $2$

चरण 3

The rank is the number of pivot columns.

$2$