If \(\begin{bmatrix}x + y&-3\\4&xy\end{bmatrix} = \begin{bmatrix}6&-3\\4&8\end{bmatrix}\), then the value of \(x^2 + y^2\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 20
Two matrices are equal when their corresponding elements are equal. Comparing the first-row, first-column and the second-row, second-column elements:
\(x + y = 6\)
\(xy = 8\)
Using \(x^2 + y^2 = (x + y)^2 - 2xy\):
\(x^2 + y^2 = 6^2 - 2(8)\)
\(x^2 + y^2 = 36 - 16 = 20\)
(Indeed x and y are 2 and 4, and \(4 + 16 = 20\).)