![Given matrices S = [[1, 2, 3], [4, 5, 6]] and Q = [[-1, 4], [0, 1], [2, 7]], compute S + Q^T.](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1775106864293-9e67c56d6fd55c20.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: Identify the given matrices S and Q. S = 1 & 2 & 3 \\ 4 & 5 & 6 Q = -1 & 4 \\ 0 & 1 \\ 2 & 7 Step 2: Compute the transpose of matrix Q, denoted as Q^T. To find the transpose, swap the rows and columns of Q. The first row of Q becomes the first column of Q^T. The second row of Q becomes the second column of Q^T. The third row of Q becomes the third column of Q^T. Q^T = -1 & 0 & 2 \\ 4 & 1 & 7 Step 3: Compute the sum S + Q^T. To add matrices, add their corresponding elements. Both S and Q^T are 2 × 3 matrices, so they can be added. S + Q^T = 1 & 2 & 3 \\ 4 & 5 & 6 + -1 & 0 & 2 \\ 4 & 1 & 7 S + Q^T = 1 + (-1) & 2 + 0 & 3 + 2 \\ 4 + 4 & 5 + 1 & 6 + 7 S + Q^T = 0 & 2 & 5 \\ 8 & 6 & 13 Step 4: Compare the result with the given options. The calculated matrix is 0 & 2 & 5 \\ 8 & 6 & 13 . This matches option A. The final answer is A. 0 & 2 & 5 \\ 8 & 6 & 13 .