CBSE Class 12 Mathematics 2026 Main Paper 65/3/3 · Q355 Marksmatrix_linear_systems
CBSE Class 12 Mathematics 2026 Main Paper 65/3/3 · Question 35 (Matrices)
A draw awards 60 vouchers worth either ₹1000 or ₹500. The number of ₹1000 vouchers plus three times the number of ₹500 vouchers equals 100. Form and solve the equations using matrices. OR For P=[[2,−1],[3,4]], Q=[[5,2],[7,4]] and R=[[2,5],[3,8]], find S with PQ−RS=0.
Alternative 1 5 Marks
A draw awards 60 vouchers worth either ₹1000 or ₹500. The number of ₹1000 vouchers plus three times the number of ₹500 vouchers equals 100. Form and solve the equations using matrices.
Answer: 40 vouchers worth ₹1000 and 20 worth ₹500.
- Let x,y count the ₹1000 and ₹500 vouchers, respectively. Then x+y=60 and x+3y=100.
- The coefficient matrix [[1,1],[1,3]] has determinant 2 and inverse [[3,−1],[−1,1]]/2.
- Multiplying the inverse by (60,100)ᵀ gives (40,20)ᵀ.
Alternative 2 5 Marks
For P=[[2,−1],[3,4]], Q=[[5,2],[7,4]] and R=[[2,5],[3,8]], find S with PQ−RS=0.
Answer: S=[[−191,−110],[77,44]].
- The equation gives S=R⁻¹PQ since det R=16−15=1.
- Compute PQ=[[3,0],[43,22]] and R⁻¹=[[8,−5],[−3,2]].
- Multiplying R⁻¹ by PQ gives S=[[−191,−110],[77,44]].