![Given A = [[3, 1], [-1, 2]], verify that A2 - 5A + 7I = 0.](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1783739871620-5d095c7fb1834cd3.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: A^2 की गणना करें। A^2 = A × A = 3 & 1 \\ -1 & 2 3 & 1 \\ -1 & 2 A^2 = (3)(3) + (1)(-1) & (3)(1) + (1)(2) \\ (-1)(3) + (2)(-1) & (-1)(1) + (2)(2) A^2 = 9 - 1 & 3 + 2 \\ -3 - 2 & -1 + 4 = 8 & 5 \\ -5 & 3 Step 2: 5A की गणना करें। 5A = 5 3 & 1 \\ -1 & 2 = 5 × 3 & 5 × 1 \\ 5 × -1 & 5 × 2 = 15 & 5 \\ -5 & 10 Step 3: 7I की गणना करें। चूंकि A एक 2 × 2 मैट्रिक्स है, I एक 2 × 2 तत्समक मैट्रिक्स होगा। I = 1 & 0 \\ 0 & 1 7I = 7 1 & 0 \\ 0 & 1 = 7 × 1 & 7 × 0 \\ 7 × 0 & 7 × 1 = 7 & 0 \\ 0 & 7 Step 4: A^2 - 5A + 7I में मानों को प्रतिस्थापित करें। A^2 - 5A + 7I = 8 & 5 \\ -5 & 3 - 15 & 5 \\ -5 & 10 + 7 & 0 \\ 0 & 7 पहले घटाव करें: = 8 - 15 & 5 - 5 \\ -5 - (-5) & 3 - 10 + 7 & 0 \\ 0 & 7 = -7 & 0 \\ 0 & -7 + 7 & 0 \\ 0 & 7 अब जोड़ करें: = -7 + 7 & 0 + 0 \\ 0 + 0 & -7 + 7 = 0 & 0 \\ 0 & 0 Step 5: परिणाम की पुष्टि करें। परिणाम एक शून्य मैट्रिक्स O है। 0 & 0 \\ 0 & 0 = O इसलिए, A^2 - 5A + 7I = O सत्यापित हो गया है। सत्यापित That's 2 down. 3 left today — send the next one.