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الجبر الخطي الأمثلة
s=[246425762352]s=⎡⎢⎣246425762352⎤⎥⎦
خطوة 1
Write as an augmented matrix for sx=0.
[246402576023520]
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.
[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.
خطوة 2.2.1
Perform the row operation R2=R2-2R1 to make the entry at 2,1 a 0.
[123202-2⋅15-2⋅27-2⋅36-2⋅20-2⋅023520]
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.
خطوة 2.3.1
Perform the row operation R3=R3-2R1 to make the entry at 3,1 a 0.
[12320011202-2⋅13-2⋅25-2⋅32-2⋅20-2⋅0]
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.
خطوة 2.4.1
Perform the row operation R3=R3+R2 to make the entry at 3,2 a 0.
[12320011200+0-1+1⋅1-1+1⋅1-2+1⋅20+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.
خطوة 2.5.1
Perform the row operation R1=R1-2R2 to make the entry at 1,2 a 0.
[1-2⋅02-2⋅13-2⋅12-2⋅20-2⋅00112000000]
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,x4∈R}