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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.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 93E
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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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