![The inverse of matrix N = [[2, 3], [1, 4]] is](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1773873128552-067393f985fbfc50.png&w=3840&q=75)
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Compute the determinant of N = 2 & 3 \\ 1 & 4 . (N) = 2 & 3 \\ 1 & 4 = 2 · 4 - 3 · 1 = 8 - 3 = 5 Since (N) = 5 ≠ 0, the inverse exists. Step 2: Apply the formula for the inverse of a 2 × 2 matrix a & b \\ c & d : a & b \\ c & d ^-1 = (1)/(ad - bc) d & -b \\ -c & a Substitute a=2, b=3, c=1, d=4, (N)=5: N^-1 = (1)/(5) 4 & -3 \\ -1 & 2 Step 3: Verify by computing N · N^-1. First row, first column: 2 · (4)/(5) + 3 · (-1)/(5) = (8)/(5) - (3)/(5) = (5)/(5) = 1 First row, second column: 2 · (-3)/(5) + 3 · (2)/(5) = (-6)/(5) + (6)/(5) = (0)/(5) = 0 Second row, first column: 1 · (4)/(5) + 4 · (-1)/(5) = (4)/(5) - (4)/(5) = (0)/(5) = 0 Second row, second column: 1 · (-3)/(5) + 4 · (2)/(5) = (-3)/(5) + (8)/(5) = (5)/(5) = 1 N · N^-1 = 1 & 0 \\ 0 & 1 = I (1)/(5)4&-3\\-1&2