Algebra 2 Question of the Day

1. Multiplying gives $\begin{bmatrix}6x-y\\-3x+5y\end{bmatrix}$, which matches the left sides of the two equations, and the right side is $\begin{bmatrix}2\\11\end{bmatrix}$. (correct answer)
2. Multiplying gives $\begin{bmatrix}6x-3y\\-x+5y\end{bmatrix}$, which matches the system.
3. The matrix must be $\begin{bmatrix}6&-3\\-1&5\end{bmatrix}$ because coefficients go in columns, not rows.
4. The vector $B$ should be $\begin{bmatrix}11\\2\end{bmatrix}$ because constants always go in decreasing order.

Explanation: This question tests your ability to verify a matrix equation representation by performing matrix multiplication and checking if it produces the original system. To verify [[6, -1], [-3, 5]] times [x, y] = [2, 11] represents the given system, multiply: (1) Row 1 times X: (6)(x) + (-1)(y) = 6x - y. (2) Row 2 times X: (-3)(x) + (5)(y) = -3x + 5y. This gives [6x - y, -3x + 5y] = [2, 11], which means 6x - y = 2 and -3x + 5y = 11, exactly matching the original system. Choice A correctly verifies by showing the multiplication produces the left sides of both equations and identifying the matching right-hand side vector. Choice C incorrectly claims coefficients go in columns not rows - this is backwards! In coefficient matrices, rows correspond to equations and columns to variables. Verification is crucial: always multiply AX mentally or on paper to ensure it produces your original system - this catches transposition errors, sign mistakes, or incorrect ordering. Matrix multiplication literally reconstructs the equations, making it a perfect self-check!