**Unformatted text preview: **rank of the augmented matrix is 4), how many solutions does this system have? (b) More generally, show that a linear system Ax = b is consistent if and only if rank A = rank( A | b ). Hint: remember that for “if and only if” statements, you have to show both directions - if Ax = b is consistent then rank A = rank( A | b ) and if rank A = rank( A | b ) then Ax = b is consistent. 6. Prove that if a vector v in R 4 is a linear combination of the vectors u and w in R 4 and if A is a 5 × 4 matrix then Av is a linear combination of Au and of Aw . 1...

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