![Given that the determinant of matrix M = [[x-3, -1], [x+2, 3]] is 5, find the value of x.](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1783930197165-9f638fda049d80cd.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: Write down the formula for the determinant of a 2 × 2 matrix. For a matrix A = a & b \\ c & d , the determinant is given by (A) = ad - bc. Step 2: Apply the determinant formula to the given matrix M. The matrix is M = x-3 & -1 \\ x+2 & 3 . Here, a = x-3, b = -1, c = x+2, and d = 3. (M) = (x-3)(3) - (-1)(x+2) Step 3: Set the determinant equal to 5 and solve for x. (x-3)(3) - (-1)(x+2) = 5 3x - 9 + (x+2) = 5 3x - 9 + x + 2 = 5 4x - 7 = 5 4x = 5 + 7 4x = 12 x = (12)/(4) x = 3 Send me the next one 📸