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Question: consider a matriz a which we transform to the matrir...

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Consider a matriz A, which we transform to the matrir 0 a 0 0 b 000 f by a series of row operations. Assume B = rref(A) (read B is the reduced Tow echelon form of A) (1) What can we say about the constants a through f? What is the first column of A? (2) In class we defined the rank of a matriz A as the number of leading 1s in rref (A). What is the (3) Suppose [A 0 is the augmented matria for a linear system. Is the system consistent? If it is, (4) Now, going further, suppose that [A (uhere 0) is the augmented matriz for a linear rank of the matriz A? how many solutions are there? system. Give one explicit erample for v such that this system is (a) inconsistent, (b) has infinity many solution, (c) has a unique solution (5) Continue to suppose that [A] ขึ] (where u 0) is the augmented rnatr for a linear systern. Can you change the last row of B so that the resulting linear system has no solutions? Can you change the last row of B to ensure that there is a unique solution?
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