![Given matrices G = [[6, 0], [-4, 2]] and H = [[9, 0], [-6, 3]], prove or disprove that 5G - 2H = 0.](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1774604367723-7a2a8fc7d326b657.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: Calculate 5G. Multiply each element of matrix G by 5. 5G = 5 6 & 0 \\ -4 & 2 = 5 × 6 & 5 × 0 \\ 5 × (-4) & 5 × 2 = 30 & 0 \\ -20 & 10 Step 2: Calculate 2H. Multiply each element of matrix H by 2. 2H = 2 9 & 0 \\ -6 & 3 = 2 × 9 & 2 × 0 \\ 2 × (-6) & 2 × 3 = 18 & 0 \\ -12 & 6 Step 3: Calculate 5G - 2H. Subtract the corresponding elements of 2H from 5G. 5G - 2H = 30 & 0 \\ -20 & 10 - 18 & 0 \\ -12 & 6 5G - 2H = 30 - 18 & 0 - 0 \\ -20 - (-12) & 10 - 6 5G - 2H = 12 & 0 \\ -20 + 12 & 4 5G - 2H = 12 & 0 \\ -8 & 4 The problem asks to show that 5G - 2H = 0. However, our calculation shows that 5G - 2H = 12 & 0 \\ -8 & 4 , which is not the zero matrix 0 & 0 \\ 0 & 0 . Therefore, the statement 5G - 2H = 0 is incorrect based on the given matrices. The final answer is The statement 5G - 2H = 0 is incorrect. 5G - 2H = 12 & 0 \\ -8 & 4 .