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: Understand the additive inverse of a matrix. The additive inverse of a matrix is found by negating each element of the matrix. If A is a matrix, its additive inverse is -A, such that A + (-A) = O, where O is the zero matrix. Step 2: Find the additive inverse of the given matrix. The given matrix is -1 & 2 \\ 3 & -4 . Its additive inverse is: -1 & 2 \\ 3 & -4 = -(-1) & -(2) \\ -(3) & -(-4) = 1 & -2 \\ -3 & 4 Step 3: Equate the calculated additive inverse with the given additive inverse. We are given that the additive inverse is a & -2 \\ -3 & b . Therefore, we can set up the equality: a & -2 \\ -3 & b = 1 & -2 \\ -3 & 4 Step 4: Compare corresponding elements to find the values of a and b. By comparing the elements in the same positions, we get: a = 1 b = 4 The values are a = 1 and b = 4. The final answer is a=1, b=4. Send me the next one 📸