A system of three linear equations a_i*x + b_i*y + c_i*z = d_i (i = 1,2,3, with a_i,b_i,c_i nonzero) has the unique solution (alpha, beta, gamma). Match the conditions in List-I with the corresponding values in List-II. List-I (I) If a_i = k and d_i = k² (k != 0) for all i, and alpha + bet

Question

A system of three linear equations a_i*x + b_i*y + c_i*z = d_i (i = 1,2,3, with a_i,b_i,c_i nonzero) has the unique solution (alpha, beta, gamma). Match the conditions in List-I with the corresponding values in List-II. List-I (I) If a_i = k and d_i = k² (k != 0) for all i, and alpha + beta + gamma = 2, then k equals (II) If a_i = d_i = k != 0 for all i, then alpha + beta + gamma equals (III) If a_i = k > 0 and d_i = k + 1 for all i, then alpha + beta + gamma can be (IV) If a_i = k < 0 and d_i = k + 1 for all i, then alpha + beta + gamma can be List-II (P) 1 (Q) 2 (R) 0 (S) 3 (T) -1

Accepted Answer

I -> P; II -> R; III -> Q,S; IV -> T. Each row has the same coefficient k multiplying x. Writing the system as k*x = d_i - (b_i*y + c_i*z), the relation between d_i and k controls x and hence the sum of the solution components.

Solution

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