If the system of linear equations : aligned & x₁+2 x₂+3 x₃=6 & x₁+3 x₂+5 x₃=9 & 2 x₁+5 x₂+a x₃=b aligned is consistent and has infinite number of solutions, then :

Step-by-step solution

Given system of equations can be written in matrix form as AX = B where A = ( array lll 1 & 2 & 3 1 & 3 & 5 2 & 5 & a array ) and B = ( array l 6 9 b array ) Since, system is consistent and has infinitely many solutions ( adj . A ) B =0 aligned & ( array ccc 3 a-25 & 15-2 a & 1 10-a & a-6 & -2 -1 & -1 & 1 array ) ( array l 6 9 b array )= ( array l 0 0 0 array ) & -6-9+b=0 b=15 & and 6(10-a)+9(a-6)-2(b)=0 & 60-6 a+9 a-54-30=0 & 3 a=24 a=8 aligned Hence, a=8, b=15 .