theorem 7 is the sentence following \"Recall Theorem 7 from class:\" AS STATED A
ID: 3169663 • Letter: T
Question
theorem 7 is the sentence following "Recall Theorem 7 from class:"
AS STATED ABOVE CLEARLY THEOREM 7 IS THE SENTENCE FOLLOWING "RECALL THEOREM 7 FROM CLASS:" THUS CLEARLY MEANING THEOREM 7 IS : IF THERE IS A NONZERO LINEAR COMBINATION OF THE COLUMNS OF A THAT EQUALS THE N X 1 COLUMN VECTOR 0 THAT DET(A)=0.
4. (3 points) Suppose A is a n × n square matrix. Recall Theorem 7 from class: If there is a nonzero linear combination of the columns of A that equals the n × 1 column vector 0 that det (A)-0. Suppose the homogeneous linear system Ax-0 has infinitely many solutions. Use this to explain why det (A)0 in light of Theorem 7Explanation / Answer
Yes ,If there exists nonzero linear combination of the columns of A , that equal column vector 0 ,then DET(A) will be 0.
*let c0,c1,c2, . . . ,cn-1 be colunmns of An*n
Given a0c0+a1c1+ . . . +an-1cn-1 = c0
=> (a0-1)c0+a1c1+ . . . +an-1cn-1 = 0
the vale of the DET dosent change by doing column operations ,
We can muliply (a0-1),a1,....an-1 to corresponding columns and add ,we get one column as 0 vector
=>DET(A)=0
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