24a. Every matrix equation Ax b corresponds to a vector b. Any linear combinatio

Question

24a. Every matrix equation Ax b corresponds to a vector b. Any linear combination of vectors can always be written c. The solution set of a linear system whose augmented equation with the same solution set. in the form Ax for a suitable matrix A and vector x. matrix is [a a2 a b] is the same as the solution set of Ax = b, if A = [ a1 a2 a3 ]. If the equation Ax set spanned by the columns of A. d. b is inconsistent, then b is not in the e. If the augmented matrix [A b] has a pivot position in every row, then the equation Ax = b is inconsistent.

Explanation / Answer

24. a. The statement is true. If A is a mxn matrix, then the solution set is x = p1 A1+p2A2+…+pnAn, where p1,p2, …,pn are scalars and A1,A2,…An are n-vectors.

     b. The statement is true. If A is a mxn matrix, then, the multiplication of A by x will yield m linear combinations of n-vectors.

     c. The statement is apparently true.

    d. The statement is True. If the system Ax = b is inconsistent then among the non-zero rows of the

          RREF of the augmented matrix [A|b], there is a row with zero everywhere except at the last place.

         Then b cannot be in Col(A).

    e. The statement is False. The equation I3x = (1,2,3)T is consistent and the augmented matrix of this equation has a pivot in each row.     

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