Use row operations on the augmented matrix as far as necessary to determine whether the system is independent, dependent, or inconsistent.4x-5y+ 4z 512x-15y+ 12z 15= 8x + 10y- 8z = - 10Is the system is independent, dependent, or inconsistent?O A. inconsistentO B. independentOC. dependent

Given: The system of linear equation as 4x-5y+4z=512x-15y+12z=15-8x+10y-8z=-10 To determine: whether the given system is independent or dependent or inconsistent.Explanation: It is known that, a system of linear equation is independent if it has unique solution, a system of equation is dependent if it has infinite solution and a system of equation is inconsistent if it has no solution. Consider it the Augmented matrix of given system of linear equation, A|b=4-54¦512-1512¦15-810-8¦-10 Applying row operation on augmented matrix, 4-54¦512-1512¦15-810-8¦-10≡4-54¦5000¦0000¦0 Performing R2→R2-3R1 and R3→R3+2R1≡1-541¦54000¦0000¦0 Performing R1→R14 As there are two zero row in reduced matrix hence the system has infinite solution, Therefore the given system is dependent. Answer: Option (C) is correct.