Question: (a) Let A be an m n matrix and let M = A | b be the augmented matrix for the linear system Ax

(a) Let A be an m × n matrix and let M = A | b be the augmented matrix for the linear system Ax = b. Show that either

(i) Rank A = rank M, or

(ii) Rank A = rank M − 1.
(b) Prove that the system is compatible if and only if case (i) holds.

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a Lets start by defining the rank of a matrix The rank of a matrix is the number of linearly independent rows or columns in the matrix In other words ... View full answer

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