Let a 225641061025 we want to determine if the system ax b...

Let A = ⎡⎣⎢−2−2−5641061025⎤⎦⎥. We want to determine if the system Ax = b has a solution for every b in ℝ³. To check this, we add -1 times the first row to the second. We then add -2 times the first row to the third. We then add times the new second row to the new third row. We conclude that: A. There is not a solution for every b in ℝ³. B. There is a solution for every b in ℝ³. C. We cannot tell if there is a solution for every b in ℝ³.

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00:01 Okay, here's the question.

00:04 Suppose a system of three linear equations and three unknowns is being solved making use of row operations.

00:13 In other words, a matrix where b is an element of the real numbers and the following matrix is obtained.

00:22 And so here's the matrix we get.

00:24 Um, all right, so we're supposed to make some speculations about how many answers there are.

00:35 Now here's the problem.

00:38 When you get those three zeros right there and we've got to figure out something about that letter.

00:46 That's not a six.

00:47 That's letter b.

00:49 Okay, so i says only one solution exists if b is equal to zero.

00:57 Only one solution exists if b is not equal to zero.

01:02 No solution exists if b is equal to zero.

01:05 And one solution exists if b is not equal to zero.

01:10 Four says no solution exists if b is not equal to zero.

01:14 And infinitely many solutions exist if b is equal to zero.

01:19 And v says none of the above.

01:22 Okay, now let me show you what those three zeros mean.

01:27 We're going to assume that our three equations are something x plus or minus something y plus or minus something z equals and then this is the answer.

01:41 Okay, so the fact that i've got those three zeros that tells me that 0x plus 0y plus 0z equals something...

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