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 is the solution to the question from the image. The vectors are given as: a = 2 \\ 7 b = m \\ -3 c = 5 \\ n The vector equation is a + 2b = c. Find the values of m and n. Step 1: Write the given vector equation. a + 2b = c Step 2: Substitute the given column vectors into the equation. 2 \\ 7 + 2 m \\ -3 = 5 \\ n Step 3: Perform the scalar multiplication. Multiply each component of vector b by 2: 2 m \\ -3 = 2m \\ 2 × (-3) = 2m \\ -6 Step 4: Perform the vector addition. Substitute the result back into the equation and add the corresponding components: 2 \\ 7 + 2m \\ -6 = 5 \\ n 2 + 2m \\ 7 + (-6) = 5 \\ n 2 + 2m \\ 1 = 5 \\ n Step 5: Equate the corresponding components. For the vectors to be equal, their x-components must be equal and their y-components must be equal. From the x-components: 2 + 2m = 5 From the y-components: 1 = n Step 6: Solve for m and n. From the y-components, we directly get: n = 1 From the x-components: 2m = 5 - 2 2m = 3 m = (3)/(2) The values are m = (3)/(2), n = 1. Last free one today — make it count tomorrow, or type /upgrade for unlimited.