Let A be an mxn matrix. Consider the following statements: 1. The set of solutions of the system of linear equations Ax=0 is a subspace of Rn. 2. The set of solutions of the system of linear equations Ax=0 is a subspace of Rm. 3. The set of solutions of the system of linear equations Ax=b, b≠0, is a subspace of Rn. 4. If u,v∈Rn are solutions of the system of linear equations Ax=0, then so is u+v.
Let A be an mxn matrix. Consider the following statements: 1. The set of solutions of the system of linear equations Ax=0 is a subspace of Rn. 2. The set of solutions of the system of linear equations Ax=0 is a subspace of Rm. 3. The set of solutions of the system of linear equations Ax=b, b≠0, is a subspace of Rn. 4. If u,v∈Rn are solutions of the system of linear equations Ax=0, then so is u+v.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let A be an mxn matrix.
Consider the following statements:
1. The set of solutions of the system of linear equations Ax=0 is a subspace of Rn.
2. The set of solutions of the system of linear equations Ax=0 is a subspace of Rm.
3. The set of solutions of the system of linear equations Ax=b, b≠0, is a subspace of Rn.
4. If u,v∈Rn are solutions of the system of linear equations Ax=0, then so is u+v.
5. If u∈Rn is a solution of the system of linear equations Ax=b, b≠0, then αu is also a solution.
Which of the following is true?
- A. Statements 1 and 2 are true.
- B. Statements 2 and 3 are true.
- C. Statements 1 and 4 are true.
- D. Statements 1 and 5 are true.
- E. Statements 4 and 5 are true.
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