| array ccc x+2 & x+3 & x+5 x+4 & x+6 & x+9 x+8 & x+11 & x+15 array | is equal to

Step-by-step solution

Let = | array lll x+2 & x+3 & x+5 x+4 & x+6 & x+9 x+8 & x+11 & x+15 array | Apply operations R₂ R₂-R₁, R₃ R₃-R₁ , we get = | array ccc x+2 & x+3 & x+5 2 & 3 & 4 6 & 8 & 10 array | Again, apply operation C₂ C₂-C₁ , C₃ C₃-C₁ , we get = | array ccc x+2 & 1 & 3 2 & 1 & 2 6 & 2 & 4 array | Expand along R₁ , we get aligned & =(x+2)(4-4)-1(8-12)+3(4-6) & =0+4+3(-2)=4-6=-2 aligned