الأمثلة
S([abc])=[a-b-ca-b-ca-b+c]S⎛⎜⎝⎡⎢⎣abc⎤⎥⎦⎞⎟⎠=⎡⎢⎣a−b−ca−b−ca−b+c⎤⎥⎦
خطوة 1
نواة التحويل هي المتجه الذي يجعل التحويل مساويًا للمتجه الصفري (الصورة السابقة للتحويل).
[a-b-ca-b-ca-b+c]=0⎡⎢⎣a−b−ca−b−ca−b+c⎤⎥⎦=0
خطوة 2
أنشئ سلسلة معادلات من معادلة المتجه.
a-b-c=0a−b−c=0
a-b-c=0a−b−c=0
a-b+c=0a−b+c=0
خطوة 3
Write the system as a matrix.
[1-1-101-1-101-110]⎡⎢
⎢⎣1−1−101−1−101−110⎤⎥
⎥⎦
خطوة 4
خطوة 4.1
Perform the row operation R2=R2-R1R2=R2−R1 to make the entry at 2,12,1 a 00.
خطوة 4.1.1
Perform the row operation R2=R2-R1R2=R2−R1 to make the entry at 2,12,1 a 00.
[1-1-101-1-1+1-1+10-01-110]⎡⎢
⎢⎣1−1−101−1−1+1−1+10−01−110⎤⎥
⎥⎦
خطوة 4.1.2
بسّط R2R2.
[1-1-1000001-110]⎡⎢
⎢⎣1−1−1000001−110⎤⎥
⎥⎦
[1-1-1000001-110]
خطوة 4.2
Perform the row operation R3=R3-R1 to make the entry at 3,1 a 0.
خطوة 4.2.1
Perform the row operation R3=R3-R1 to make the entry at 3,1 a 0.
[1-1-1000001-1-1+11+10-0]
خطوة 4.2.2
بسّط R3.
[1-1-1000000020]
[1-1-1000000020]
خطوة 4.3
Swap R3 with R2 to put a nonzero entry at 2,3.
[1-1-1000200000]
خطوة 4.4
Multiply each element of R2 by 12 to make the entry at 2,3 a 1.
خطوة 4.4.1
Multiply each element of R2 by 12 to make the entry at 2,3 a 1.
[1-1-10020222020000]
خطوة 4.4.2
بسّط R2.
[1-1-1000100000]
[1-1-1000100000]
خطوة 4.5
Perform the row operation R1=R1+R2 to make the entry at 1,3 a 0.
خطوة 4.5.1
Perform the row operation R1=R1+R2 to make the entry at 1,3 a 0.
[1+0-1+0-1+1⋅10+000100000]
خطوة 4.5.2
بسّط R1.
[1-10000100000]
[1-10000100000]
[1-10000100000]
خطوة 5
Use the result matrix to declare the final solution to the system of equations.
a-b=0
c=0
0=0
خطوة 6
Write a solution vector by solving in terms of the free variables in each row.
[abc]=[bb0]
خطوة 7
Write the solution as a linear combination of vectors.
[abc]=b[110]
خطوة 8
Write as a solution set.
{b[110]|b∈R}
خطوة 9
The solution is the set of vectors created from the free variables of the system.
{[110]}
خطوة 10
نواة S هي الفضاء الجزئي {[110]}.
K(S)={[110]}
