A = [aᵢⱼ] is a 2 × 2 matrix with aᵢⱼ = ((i + j)^2)/2. Which matrix is A?

Question 13

MediumOriginal question

$A = [a_{ij}]$ is a 2 × 2 matrix with $a_{ij} = \frac{(i + j)^2}{2}$ . Which matrix is $A$ ?

\begin{bmatrix}4 & 9 \\ 9 & 16\end{bmatrix}

Correct answerYour answer

\begin{bmatrix}1 & \frac{9}{2} \\ \frac{9}{2} & 8\end{bmatrix}

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\begin{bmatrix}2 & \frac{9}{2} \\ \frac{9}{2} & 8\end{bmatrix}

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\begin{bmatrix}2 & 4 \\ 4 & 8\end{bmatrix}

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$a_{11} = \frac{4}{2} = 2$ , $a_{12} = a_{21} = \frac{9}{2}$ , $a_{22} = \frac{16}{2} = 8$ .
So $A = \begin{bmatrix} 2 & \frac{9}{2} \\ \frac{9}{2} & 8 \end{bmatrix}$ .

Worth noting

Leaving out the division by 2 gives the squares 4, 9, 9, 16 themselves.

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