12th Maths Guide Solution Application of Matrices and Determinants Exercise 1.7

Question no 1: Solve the following system of homogeneous equations.

(i) 3x + 2y + 7z = 0; 4x – 3y – 2z = 0; 5x + 9y + 23z = 0

Solution:-

(ii) 2x + 3y – z = 0, x – y – 2z = 0, 3x + y + 3z = 0

Solution:-

Question no 2: Determine the values of λ for which the following system of equations.

x + y + 3z = 0; 4x + 3y + λz = 0, 2x + y + 2z = 0 has

(i) a unique solution
(ii) a non-trivial solution.

Solution:-

Question no 3: By using Gaussian elimination method, balance the chemical reactions equation.
C₂H₆ + O₂ → H₂O + CO₂.

Solution:-