Suppose we have the linear system a11 x1 + a12 x2 = b1 a21 x1 + a22 x2 = b2. The
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Question
Suppose we have the linear system a11 x1 + a12 x2 = b1 a21 x1 + a22 x2 = b2. The augmented matrix for this system is In lecture, we saw that it can useful to manipulate such an augmented matrix to give a new augmented matrix with nice properties, in this case so that the (2,1) entry is zero. For this example, this can be accomplished by the replacing second row of the augmented matrix with one obtained by summing a multiple of the first row and a multiple of the second row. Please assume that the (2,1) entry of the input matrix is non-zero. This is useful because the new augmented matrix corresponds to the linear system a11 x1 + a12 x2 = b1 c x2 = d for some c and d, which, using the method of back substitution, has the solution x2 = d / c x1 = (b1 - a12 d / c)/a11. Write a Matlab function called elimination.m which takes a 2x3 augmented matrix as input, and returns an augmented matrix for which the first row is the same as for the input matrix, and the second row is obtained by summing a multiple of the first row and a multiple of the second row chosen so that the (2,1) entry equals zero.Explanation / Answer
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