# SOLVING SYSTEM OF LINEAR EQUATIONS USING RANK METHOD WORKSHEET

(1)  Test for consistency and if possible, solve the following systems of equations by rank method.

(i)  x − y + 2z = 2, 2x + y + 4z = 7, 4x − y + z = 4    Solution

(ii)  3x + y + z = 2, x − 3y + 2z =1, 7x − y + 4z = 5

(iii)  2x + 2y + z = 5, x − y + z =1, 3x + y + 2z = 4   Solution

(iv)  2x − y + z = 2, 6x − 3y + 3z = 6, 4x − 2y + 2z = 4

Solution

(2)  Find the value of k for which the equations kx − 2y + z =1, x − 2ky + z = −2, x − 2y + kz =1 have

(i) no solution (ii) unique solution (iii) infinitely many solution          Solution

(3)  Investigate the values of λ and m the system of linear equations 2x + 3y + 5z = 9 , 7x + 3y − 5z = 8, 2x + 3y + λz = μ , have

(i) no solution (ii) a unique solution (iii) an infinite number of solutions         Solution

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