![Find the inverse of A = [[2, -1], [-3, 4]]](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1781183156619-94d249c85b8e1ca4.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
Here's how to find the inverse of matrix A: Given matrix A = 2 & -1 \\ -3 & 4 . Step 1: Calculate the determinant of matrix A. For a 2 × 2 matrix a & b \\ c & d , the determinant is ad-bc. (A) = (2)(4) - (-1)(-3) (A) = 8 - 3 (A) = 5 Step 2: Find the adjugate matrix (also known as the adjoint matrix). For a 2 × 2 matrix a & b \\ c & d , the adjugate is d & -b \\ -c & a . adj(A) = 4 & -(-1) \\ -(-3) & 2 adj(A) = 4 & 1 \\ 3 & 2 Step 3: Calculate the inverse matrix A^-1. The formula for the inverse of a 2 × 2 matrix is A^-1 = (1)/((A)) adj(A). A^-1 = (1)/(5) 4 & 1 \\ 3 & 2 Step 4: Multiply the scalar (1)/(5) by each element in the adjugate matrix. A^-1 = (4)/(5) & (1)/(5) \\ (3)/(5) & (2)/(5) The final answer is (4)/(5) & (1)/(5) \\ (3)/(5) & (2)/(5) . That's 3 down. 2 left today — send the next one.