Math Problem Statement
Giải hệ phương trình tuyến tính ⎧⎩⎨⎪⎪⎪⎪x−y+3z+2t=12x+2y−z+t=23x−3y+2z−2t=−24x−2z−3t=−1.{x−y+3z+2t=12x+2y−z+t=23x−3y+2z−2t=−24x−2z−3t=−1. Kết quả là:
Select one:
A.
x=−528+528α,y=−34−54α,z=17−87α,t=α (α∈R)x=−528+528α,y=−34−54α,z=17−87α,t=α (α∈R)
B.
Hệ phương trình vô nghiệm
C.
x=528+528α,y=34−54α,z=−17−87α,t=α (α∈R)x=528+528α,y=34−54α,z=−17−87α,t=α (α∈R)
D.
x=328+528α,y=54−54α,z=57−87α,t=α (α∈R)
Solution
We are given a system of linear equations:
x - y + 3z + 2t = 1 \\ 2x + 2y - z + t = 2 \\ 3x - 3y + 2z - 2t = -2 \\ 4x - 2z - 3t = -1 \end{cases}$$ To solve this system, we will proceed step by step, using methods such as Gaussian elimination or matrix reduction. ### Step 1: Write the system as anAsk a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
System of Linear Equations
Formulas
Gaussian Elimination
Matrix Reduction
Theorems
The Rank-Nullity Theorem
Solutions to Systems of Linear Equations
Suitable Grade Level
Grades 10-12
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