إدخال مسألة...
الجبر الخطي الأمثلة
[2113]
خطوة 1
Write as an augmented matrix for Ax=0.
[210130]
خطوة 2
خطوة 2.1
Multiply each element of R1 by 12 to make the entry at 1,1 a 1.
خطوة 2.1.1
Multiply each element of R1 by 12 to make the entry at 1,1 a 1.
[221202130]
خطوة 2.1.2
بسّط R1.
[1120130]
[1120130]
خطوة 2.2
Perform the row operation R2=R2−R1 to make the entry at 2,1 a 0.
خطوة 2.2.1
Perform the row operation R2=R2−R1 to make the entry at 2,1 a 0.
⎡⎣11201−13−120−0⎤⎦
خطوة 2.2.2
بسّط R2.
⎡⎣11200520⎤⎦
⎡⎣11200520⎤⎦
خطوة 2.3
Multiply each element of R2 by 25 to make the entry at 2,2 a 1.
خطوة 2.3.1
Multiply each element of R2 by 25 to make the entry at 2,2 a 1.
⎡⎣112025⋅025⋅5225⋅0⎤⎦
خطوة 2.3.2
بسّط R2.
[1120010]
[1120010]
خطوة 2.4
Perform the row operation R1=R1−12R2 to make the entry at 1,2 a 0.
خطوة 2.4.1
Perform the row operation R1=R1−12R2 to make the entry at 1,2 a 0.
[1−12⋅012−12⋅10−12⋅0010]
خطوة 2.4.2
بسّط R1.
[100010]
[100010]
[100010]
خطوة 3
Use the result matrix to declare the final solution to the system of equations.
x=0
y=0
خطوة 4
Write a solution vector by solving in terms of the free variables in each row.
[xy]=[00]
خطوة 5
Write as a solution set.
{[00]}