الجبر الخطي الأمثلة

$[\begin{array}{c} 11 & - 8 \\ - 17 & - 11 \\ 8 & - 12 \\ - 2 x & 3 \end{array}] + [\begin{array}{c} - 3 & 3 \\ - 17 & 12 \\ - 19 & 8 \\ - 15 & 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 1

اجمع العناصر المتناظرة.

$[\begin{array}{c} 11 - 3 & - 8 + 3 \\ - 17 - 17 & - 11 + 12 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 2

Simplify each element.

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خطوة 2.1

اطرح $3$ من $11$ .

$[\begin{array}{c} 8 & - 8 + 3 \\ - 17 - 17 & - 11 + 12 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 2.2

أضف $- 8$ و $3$ .

$[\begin{array}{c} 8 & - 5 \\ - 17 - 17 & - 11 + 12 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 2.3

اطرح $17$ من $- 17$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & - 11 + 12 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 2.4

أضف $- 11$ و $12$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & 1 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 2.5

اطرح $19$ من $8$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & 1 \\ - 11 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 2.6

أضف $- 12$ و $8$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & 1 \\ - 11 & - 4 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 2.7

أضف $3$ و $2$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & 1 \\ - 11 & - 4 \\ - 2 x - 15 & 5 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 3

اطرح العناصر المتناظرة.

$[\begin{array}{c} 8 + 13 & - 5 - 18 \\ - 34 - 11 & 1 + 16 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 4

Simplify each element.

انقر لعرض المزيد من الخطوات...

خطوة 4.1

أضف $8$ و $13$ .

$[\begin{array}{c} 21 & - 5 - 18 \\ - 34 - 11 & 1 + 16 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 4.2

اطرح $18$ من $- 5$ .

$[\begin{array}{c} 21 & - 23 \\ - 34 - 11 & 1 + 16 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 4.3

اطرح $11$ من $- 34$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 1 + 16 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 4.4

أضف $1$ و $16$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 4.5

اطرح $0$ من $- 11$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 4.6

أضف $- 4$ و $18$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 4.7

اطرح $13$ من $- 15$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 2 x - 28 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 4.8

أضف $5$ و $7$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 2 x - 28 & 12 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

خطوة 5

Write as a linear system of equations.

$21 = 21$

$- 23 = - 23$

$- 45 = - 45$

$17 = 17$

$- 11 = - 11$

$14 = 14$

$- 2 x - 28 = - 24$

$12 = 12$

خطوة 6

Since $12 = 12$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying $- 2 x - 28 = - 24$ .