UPSC NDA I 2017 Mathematics Solved Paper

Concept:The order of a matrix product is determined by the inner dimensions: multiplication is valid if they match, and the resulting order is given by the outer dimensions.Explanation:We have three matrices: $[x \; y \; z]$ (order $1 \times 3$), $\begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix}$ (order $3 \times 3$), and $\begin{bmatrix} x \\ y \\ z \end{bmatrix}$ (order $3 \times 1$).First, multiply the $1 \times 3$ matrix with the $3 \times 3$ matrix. The inner dimension (3) matches, so the result is of order $1 \times 3$.Then multiply this $1 \times 3$ result with the $3 \times 1$ matrix. Again the inner dimension (3) matches, giving a final product of order $1 \times 1$.Thus, the overall order is $1 \times 1$.Answer:$1 \times 1$ (Option B)