Consider a system of linear equations with coefficient matrix A and augmented matrix G. We know...

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Consider a system of linear equations with coefficient matrix A and augmented matrix G. We know that G is a 5 x 5 matrix. (a) The system has 5 variables and 5 equations. (b) If the reduced row-echelon form of G is the identity matrix, then the system is inconsis- tent. (c) If the system is consistent, then every row-echelon form of G has a row of zeros. T F (e) If rank(A) T F (d) If the system has a unique solution, then every row-echelon form of A has no zero rows. T F = 4, then the system is consistent. T F (f) If the system is homogeneous, then rank(G) ≤ 4. (g) If rank(G) = 3, then the system has infinitely many solutions. (h) If rank(A) = rank(G), then the system is consistent. T F T F T F T F Consider a system of linear equations with coefficient matrix A and augmented matrix G. We know that G is a 5 x 5 matrix. (a) The system has 5 variables and 5 equations. (b) If the reduced row-echelon form of G is the identity matrix, then the system is inconsis- tent. (c) If the system is consistent, then every row-echelon form of G has a row of zeros. T F (e) If rank(A) T F (d) If the system has a unique solution, then every row-echelon form of A has no zero rows. T F = 4, then the system is consistent. T F (f) If the system is homogeneous, then rank(G) ≤ 4. (g) If rank(G) = 3, then the system has infinitely many solutions. (h) If rank(A) = rank(G), then the system is consistent. T F T F T F T F

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