Question

question 13
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is the element $a_{i, n - i + 1}$ of the identity matrix $i_{n}$ equal to 1?
true
false

Explanation:

Step1: Recall Identity Matrix Definition

An identity matrix \( I_{[n]} \) is an \( n \times n \) matrix where the diagonal elements (where row index \( i \) equals column index \( j \), i.e., \( a_{i,j} = 1 \) when \( i = j \)) and all non - diagonal elements are 0.

Step2: Analyze the Element \( a_{i, n - i+1} \)

We want to check when \( i=n - i + 1\). Solving the equation \( i=n - i + 1\) for \( i\):

$$
LATEXBLOCK0
$$

This means that \( a_{i,n - i+1}=1 \) only when \( i=\frac{n + 1}{2}\) (i.e., when \( n\) is odd and \( i\) is the middle row/column index). For other values of \( i\), \( i
eq n - i + 1\), so \( a_{i,n - i+1}=0\). Since the question is asking if \( a_{i,n - i+1}\) is always equal to 1 (for any \( i\) and \( n\)), the answer is no.

Answer:

False