MATH307 April 2006
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Question 01 (b)
Let PA = LU be
(b) Find the condition on b1, b2, and b3 so that Ax = b has at least one solution.
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To find the condition on , let us first solve the matrix problem .
Since we are given the LU decomposition and partial pivoting of matrix A, we can simply follow the steps described by the matrix P (swapping the second and third row which is highlighted in ) and L (subtracting twice the first row () from the third row and subtracting once the second row from the third row()), we would arrive at
In order for to have at least solution, the above matrix must be consistent, therefore the last row must contain all zeros.
The constraint on is the equation .