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This question examines your understanding of the connection between linear systems and matrices. Please tick all correct statements. (Try to deduce the statements from facts you know, or try to find counterexamples, i.e. find examples showing that the statements are false.) You gain marks for every correct statement you tick, and you lose marks for every incorrect statement you tick. In total, the lowest number of marks you can score for this question is zero. (If you tick more incorrect than correct statements, your marks for this question will be set to zero.) a. Let A in Rnxn be such that rank(A)=n, and let b in Rn. Then the linear system Ax=b possesses at least one solution. b. Let m>n, let A in Rmxn be such that rank(A)=n, and let b in Rm. Then the linear system Ax=b possesses at most one solution. O c. Let m>n, let A in Rmxn be such that rank(A)=n, and let b in Rm. Then the linear system Ax=b possesses at least one solution. Od. Let A in Rnxn be such that rank(A)=n, and let b in Rn. Then the linear system Ax=b possesses at most one solution.

This question examines your understanding of the connection between linear systems and matrices. Please tick all correct statements. (Try to deduce the statements from facts you know, or try to find counterexamples, i.e. find examples showing that the statements are false.) You gain marks for every correct statement you tick, and you lose marks for every incorrect statement you tick. In total, the lowest number of marks you can score for this question is zero. (If you tick more incorrect than correct statements, your marks for this question will be set to zero.) a. Let A in Rnxn be such that rank(A)=n, and let b in Rn. Then the linear system Ax=b possesses at least one solution. b. Let m>n, let A in Rmxn be such that rank(A)=n, and let b in Rm. Then the linear system Ax=b possesses at most one solution. O c. Let m>n, let A in Rmxn be such that rank(A)=n, and let b in Rm. Then the linear system Ax=b possesses at least one solution. Od. Let A in Rnxn be such that rank(A)=n, and let b in Rn. Then the linear system Ax=b possesses at most one solution.

Advanced Engineering Mathematics
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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This question examines your understanding of the connection between linear systems and matrices. Please tick all correct statements. (Try to deduce the statements from facts you know, or try to find counterexamples, i.e. find examples showing that the statements are false.) You gain marks for every correct statement you tick, and you lose marks for every incorrect statement you tick. In total, the lowest number of marks you can score for this question is zero. (If you tick more incorrect than correct statements, your marks for this question will be set to zero.) Let A in Rnxn be such that rank(A)=n, and let b in Rn. Then the linear system Ax=b possesses at least one solution. O b. Let m>n, let A in Rmxn be such that rank(A)=n, and let b in Rm. Then the linear system Ax=b possesses at most one solution. ☐ c. Let m>n, let A in Rmxn be such that rank(A)=n, and let b in Rm. Then the linear system Ax=b possesses at least one solution. O d. Let A in Rnxn be such that rank(A)=n, and let b in Rn. Then the linear system Ax=b possesses at most one solution. a.
Transcribed Image Text:This question examines your understanding of the connection between linear systems and matrices. Please tick all correct statements. (Try to deduce the statements from facts you know, or try to find counterexamples, i.e. find examples showing that the statements are false.) You gain marks for every correct statement you tick, and you lose marks for every incorrect statement you tick. In total, the lowest number of marks you can score for this question is zero. (If you tick more incorrect than correct statements, your marks for this question will be set to zero.) Let A in Rnxn be such that rank(A)=n, and let b in Rn. Then the linear system Ax=b possesses at least one solution. O b. Let m>n, let A in Rmxn be such that rank(A)=n, and let b in Rm. Then the linear system Ax=b possesses at most one solution. ☐ c. Let m>n, let A in Rmxn be such that rank(A)=n, and let b in Rm. Then the linear system Ax=b possesses at least one solution. O d. Let A in Rnxn be such that rank(A)=n, and let b in Rn. Then the linear system Ax=b possesses at most one solution. a.
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