If [ array lll 1 & 3 & 3 1 & 4 & 4 1 & 3 & 4 array ] [ array l x y z array ]= [ array l 12 15 13 array ] , then the value of x^2+y^2+z^2=

Step-by-step solution

The matrix equation corresponds to the system: x + 3y + 3z = 12 x + 4y + 4z = 15 x + 3y + 4z = 13 Subtracting the first equation from the second gives: y + z = 3 . Subtracting the first from the third yields: z = 1 . Substituting z = 1 into y + z = 3 gives y = 2 . Then, from the first equation: x + 3(2) + 3(1) = 12 , so x = 3 . Thus, x² + y² + z² = 3² + 2² + 1² = 9 + 4 + 1 = 14 . Final answer: D