Class 12 Determinants · Short Answer2 Marksmatrix_method_linear_systems
Class 12 Maths · Determinants · Short Answer #91
Solve 3x+y=19 and 3x−y=23 by the matrix method.
✅ Step-by-Step Solution
Final Answer: x=7,y=−2
- Write MX=B with M=[[3,1],[3,−1]], X=[x,y]ᵀ and B=[19,23]ᵀ.
- det(M)=−6≠0, so M⁻¹=(−1/6)[[−1,−1],[−3,3]]. Multiply by B to get (−1/6)[−42,12]ᵀ=[7,−2]ᵀ.
- Therefore x=7,y=−2; these satisfy both equations.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write MX=B with M=[[3,1],[3,−1]], X=[x,y]ᵀ and B=[19,23]ᵀ.
- [1 mark] det(M)=−6≠0, so M⁻¹=(−1/6)[[−1,−1],[−3,3]]. Multiply by B to get (−1/6)[−42,12]ᵀ=[7,−2]ᵀ.
- [0.5 marks] Therefore x=7,y=−2; these satisfy both equations.
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