Linear Algebra Question: Below, five systems of linear equations have been put i

Question

Linear Algebra Question:

Below, five systems of linear equations have been put in reduced row echelon form. Identify how many solutions each one has, and enter that number in the blank. Enter the word "infinite" (without the quote marks) if there are infinitely many solutions. (a) ___________ [1 5 5 -5 0 2 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|1 -5 0 0 0] (b) ________[1 0 0 -5 0 1 0 -2 0 0 1 4 0 0 0 0 0 0 0 0|1 -2 -4 0 0] (c) ______ [1 -3 -1 0 5 -5 0 0 0 1 -4 4 0 0 0 0 0 0 |2 -1 1] (d) ______ [1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 |-1 3 4 3 0] (e) ________ [1 0 0 0 1 0 0 0 1 0 0 0|-5 2 0 0]

Explanation / Answer

a) infinite many solutions

b) infinite many solutions

c) the system has no solution as it contains leading entry in last column

d) one solution

e) if the last column does not contain any leading entry then and all other columns contain a leading entry

then this has exactly one solution

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