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

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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