NDA 1 2025 Maths, question 23

Topic: Matrices and determinants

Q23

If $\begin{bmatrix} x & 1 & 1 \end{bmatrix}\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}\begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix} = \begin{bmatrix} 45 \end{bmatrix}$ , then which one of the following is a value of $x$ ?

(a) -2
(b) -1
(c) 0
(d) 1Correct answer

Solution.

Answer: (d) 1

Multiply the matrix by the column first to obtain $(3 + 3x,\ 9 + 6x,\ 15 + 9x)^{T}$ .
The row product then gives $3x^{2} + 18x + 24 = 45$ .
Thus $x^{2} + 6x - 7 = (x - 1)(x + 7) = 0$ .
The listed root is $x = 1$ .