![Find the determinant of M = [[3, -5, -5], [-6, -3, -3], [2, 2, 1]]. If P = [[8, 3], [-9, 2]], find P inverse.](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1788084426244-c8ff9d16aa1db282.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 are the solutions to your matrix problems. Question 2: Find the determinant of M = 3 & -5 & -5 \\ -6 & -3 & 2 \\ 2 & 2 & 1 . Step 1: Write the formula for the determinant of a 3 × 3 matrix. For a matrix a & b & c \\ d & e & f \\ g & h & i , the determinant is a(ei - fh) - b(di - fg) + c(dh - eg). Step 2: Substitute the values from matrix M into the formula. (M) = 3((-3)(1) - (2)(2)) - (-5)((-6)(1) - (2)(2)) + (-5)((-6)(2) - (-3)(2)) Step 3: Calculate the terms inside the parentheses. (M) = 3(-3 - 4) + 5(-6 - 4) - 5(-12 - (-6)) (M) = 3(-7) + 5(-10) - 5(-12 + 6) (M) = 3(-7) + 5(-10) - 5(-6) Step 4: Perform the multiplications and additions. (M) = -21 - 50 + 30 (M) = -71 + 30 (M) = -41 The determinant of M is -41. Question 1b: If P = 8 & 3 \\ -9 & 2 , find P^-1 (the inverse of P). Step 1: Calculate the determinant of matrix P. For a 2 × 2 matrix a & b \\ c & d , the determinant is ad - bc. (P) = (8)(2) - (3)(-9) (P) = 16 - (-27) (P) = 16 + 27 (P) = 43 Step 2: Write the formula for the inverse of a 2 × 2 matrix. P^-1 = (1)/((P)) d & -b \\ -c & a Step 3: Substitute the values into the inverse formula. P^-1 = (1)/(43) 2 & -3 \\ -(-9) & 8 P^-1 = (1)/(43) 2 & -3 \\ 9 & 8 Step 4: Multiply each element by (1)/(43). P^-1 = (2)/(43) & (-3)/(43) \\ (9)/(43) & (8)/(43) The inverse of P is (2)/(43) & (-3)/(43) \\ (9)/(43) & (8)/(43) . Send me the next one 📸