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Question: If $\begin{bmatrix} 6 & -31 & 1 \\ 4 & 31 & -1 \\ 20 & 3 & 1 \end{bmatrix}$ = x+y, then (x,y) is...

If [6−311431−12031]\begin{bmatrix} 6 & -31 & 1 \\ 4 & 31 & -1 \\ 20 & 3 & 1 \end{bmatrix} = x+y, then (x,y) is

A

(2,3)

B

(1,2)

C

(3,1)

D

(0,0)

Answer

(1,2)

Explanation

Solution

The problem states a matrix equals x+y. This implies x+y is a scalar value derived from the matrix. By calculating various scalar properties of the matrix (determinant, trace, sum of all elements, sum of rows/columns), we find that the sum of the elements in the second column is 3. Among the given options, only (1,2) yields a sum of 3 (1+2=3). Therefore, it is inferred that the question implicitly asks for x+y to be the sum of the elements of the second column.