Determine the value of h such that the matrix is the augmented matrix of a consistent linear system

Determine the value of h such that the matrix is the augmented matrix of a consistent linear system. I need help with both of the problems below.

1. [ 6 4 h] [-3 -2 7]

2. [1 2 -4] [3 h -12]

Answer

Consider the augmented matrix, -3 -27 From the last matrix, observe that, rank(A)-1 and rank (A b) lif 14+h0 Recall the fact

Consider the augmented matrix, 1 2 A3h-12 RR-3R 1 2 -4 0 h-6 0 From the last matrix, observe that, rank(A)-rank([A b]) for an

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