الجبر الخطي الأمثلة

أوجد فضاء العينة s=[[2,4,6,4],[2,5,7,6],[2,3,5,2]]
s=[246425762352]s=246425762352
خطوة 1
Write as an augmented matrix for sx=0.
[246402576023520]
خطوة 2
أوجِد الصيغة الدرجية المختزلة صفيًا.
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خطوة 2.1
Multiply each element of R1 by 12 to make the entry at 1,1 a 1.
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خطوة 2.1.1
Multiply each element of R1 by 12 to make the entry at 1,1 a 1.
[22426242022576023520]
خطوة 2.1.2
بسّط R1.
[123202576023520]
[123202576023520]
خطوة 2.2
Perform the row operation R2=R2-2R1 to make the entry at 2,1 a 0.
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خطوة 2.2.1
Perform the row operation R2=R2-2R1 to make the entry at 2,1 a 0.
[123202-215-227-236-220-2023520]
خطوة 2.2.2
بسّط R2.
[123200112023520]
[123200112023520]
خطوة 2.3
Perform the row operation R3=R3-2R1 to make the entry at 3,1 a 0.
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خطوة 2.3.1
Perform the row operation R3=R3-2R1 to make the entry at 3,1 a 0.
[12320011202-213-225-232-220-20]
خطوة 2.3.2
بسّط R3.
[12320011200-1-1-20]
[12320011200-1-1-20]
خطوة 2.4
Perform the row operation R3=R3+R2 to make the entry at 3,2 a 0.
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خطوة 2.4.1
Perform the row operation R3=R3+R2 to make the entry at 3,2 a 0.
[12320011200+0-1+11-1+11-2+120+0]
خطوة 2.4.2
بسّط R3.
[123200112000000]
[123200112000000]
خطوة 2.5
Perform the row operation R1=R1-2R2 to make the entry at 1,2 a 0.
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خطوة 2.5.1
Perform the row operation R1=R1-2R2 to make the entry at 1,2 a 0.
[1-202-213-212-220-200112000000]
خطوة 2.5.2
بسّط R1.
[101-200112000000]
[101-200112000000]
[101-200112000000]
خطوة 3
Use the result matrix to declare the final solution to the system of equations.
x1+x3-2x4=0
x2+x3+2x4=0
0=0
خطوة 4
Write a solution vector by solving in terms of the free variables in each row.
[x1x2x3x4]=[-x3+2x4-x3-2x4x3x4]
خطوة 5
Write the solution as a linear combination of vectors.
[x1x2x3x4]=x3[-1-110]+x4[2-201]
خطوة 6
Write as a solution set.
{x3[-1-110]+x4[2-201]|x3,x4R}
(
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)
|
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[
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{
{
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A
A
7
7
8
8
9
9
B
B
4
4
5
5
6
6
/
/
^
^
×
×
>
>
π
π
1
1
2
2
3
3
-
-
+
+
÷
÷
<
<
!
!
,
,
0
0
.
.
%
%
=
=
 [x2  12  π  xdx ]